Peter R.
Johnston
,
Dianne J.
Watters
,
Christopher L.
Brown
and
Wendy A.
Loughlin
*
School of Natural Sciences, Griffith University, Brisbane, Queensland 4111, Australia. Email: w.loughlin@griffith.edu.au
First published on 13th September 2016
An online Maths Skills Site was developed as an integrated support programme for first year Chemistry students, the content of which, was based on an analysis of their highschool mathematical backgrounds. This study examined the students’ perceptions of Maths, their patterns of usage of the Maths Skills Site and whether there was a relationship between usage of the site and performance in first year chemistry. A questionnaire and surveys were administered to obtain data on student perceptions, confidence and anxiety. Hitcount tracking was enabled for the Maths Skills Site items (notes, questions, answers, online multiple choice questions), to establish usage patterns for the cohort and individuals, over time and against topic (significant figures, algebra, etc.). Student perceptions changed over the semester. Increased confidence with chemistry and mathematics was observed, however, a significant proportion were still anxious when having to answers questions requiring calculations. Students who were already confident did not use the Maths Skills Site, whereas the students who did use the site displayed improved achievements in the credit grade category, as compared to nonusers and employed a selfdirected approach, tailoring their individual learning around topics important to them.
The problem is exacerbated with the removal of mathematics as a prerequisite for studies in the sciences in some institutions, which has a negative impact on progression of students through university mathematics programmes and other programmes where the application of mathematics is important (King and Cattlin, 2015). It has been reported that high school courses in physics, chemistry and biology prepare students for college courses in the same discipline, which is not surprising. Furthermore, the study of advanced mathematics was also a significant predictor of performance across all college science subjects including introductory biology (Sadler and Tai, 2007). In a more recent study, the level of high school mathematics undertaken, and the grade achieved, were found to be predictive of overall pass rates in a number of STEM degree programmes (Nakakoji et al., 2014).
The decline in the number of Australian students taking more advanced mathematics subjects at high school has previously been highlighted (McPhan et al., 2008). The Queensland Studies Authority provides a context for a flat enrolment trend in mathematics in Queensland high schools over the last 10 years (Queensland Studies Authority, 2014). In addition, there has been a slight upward trend in higher level Maths C enrolments since 2009, which can be attributed to the bonus point scheme being offered by some Universities for students who have studied the advanced subject, Maths C (including vectors, matrices, real and complex numbers) (Queensland Studies Authority, 2014). However, the number of students taking Maths A (basic: financial maths, applied geometry, elementary statistics and probability) exceeds that of the other two mathematics subjects combined and there is a consistent migration from Maths B (intermediate: including functions, calculus, exponential and log functions, applied statistics) into Maths A in year 12, the final year of school (Queensland Studies Authority, 2015).
The problem of mathematics deficiency and the impact on subjects such as chemistry, starts even before university. An investigation into why high school chemistry students have difficulty with chemistry calculations showed that this was due to a lack of understanding of basic mathematical operations such as division and multiplication, fractions and ratios (Scott, 2012). Of even greater concern is the report that science graduates (particularly in the biosciences), lack quantitative skills, so not only are they coming to university with inadequate mathematical skills, they are also leaving with a lack of mathematical skills (Matthews et al., 2013).
In a comprehensive review of factors affecting student performance in physical chemistry, it was found that the strong predictors of student success are mathematical proficiency and logical thinking skills (Bain et al., 2014; Bain and Towns, 2016). Another school of thought proposes that it is not deficiencies in mathematics per se which affects student performance in chemistry, but the inability to transfer between mathematical and chemistry contexts (Becker and Towns, 2012 and references therein). Hoban et al. (2013) examined this question in detail and concluded that student difficulties were not due to an inability to transfer mathematical knowledge but due to lack of the necessary mathematical knowledge. They also found that students who are able to explain their answers of a mathematical item in a maths context are able to transfer to an equivalent item in a chemistry context.
Maths anxiety is known to affect performance (Ashcraft and Moore, 2009), as is student confidence (Parsons et al., 2009). Many students are demotivated by any activity that requires quantitative skills (Quinnell et al., 2013). A recent study (Tariq et al., 2013) examined the roles that emotional intelligence (EI; the cognitive ability to perceive, use, understand, and regulate emotional stressors) and emotional selfefficacy (ESE; confidence to use emotional competencies) play on undergraduates’ mathematical literacy. They found that EI and ESE play a greater role in performance for female students compared to male students. Thus, enhancing students’ emotional capabilities may lead to improvements in learning strategies and increased mathematics literacy. Another study (Nicholson et al., 2013) reported that students who were confident, who held realistic views of undergraduate study and who took responsibility for their own learning had higher academic performance. While confidence is positively correlated with achievement, there is also the phenomenon of the Dunning Kruger effect, whereby poorly performing students grossly overestimate their own abilities (i.e. they don’t know what they don’t know) and hence are not able to improve (Pazicni and Bauer, 2014). Sadly, this metacognitive deficiency persisted over time and was more pronounced in males than females.
For STEM students, including chemistry students, who do not have the required prerequisite knowledge, many universities offer short mathematics bridging courses before the beginning of first semester. These courses offer considerable challenges to teachers in conveying complex mathematical concepts to a diverse group of students in a short period of time (from one to a few weeks) (Gordon and Nicholas, 2010). From the student's perspective these courses appear to help with their approaches to learning mathematics, reducing anxiety and increasing confidence (Gordon and Nicholas, 2013), however there is a limit to what can be achieved in such a short time (Nicholas et al., 2015).
In recent years, a range of maths support centres and online approaches have emerged (Croft, 2000; Jackson and Johnson, 2013; Mac an Bhaird et al., 2013) which are often stand alone and are not embedded within any specific discipline. Our support programme was inspired by the Maths Skills programme developed at another Australian University; La Trobe University (Jackson and Johnson, 2013), where an extracurricular programme was introduced and tailored to support large enrolment first year courses with a diverse cohort of students. The La Trobe programme offered the choice of three learning modes – online delivery, worksheets and dropin sessions. The emphasis was on discipline relevance and mathematical problem solving in context. Student perceptions of the support programme were positive with participating students selfreporting increased confidence, increased appreciation of the relevance of mathematics to their disciplines and improved mathematical skills. A positive correlation was found between engagement with the programme and success in completion of the respective science courses. However, participation levels were low, typically engaging only from 9–18% of the student enrolments. The authors also reported difficulty in determining whether those students who most needed support, participated. Another study in Ireland (Ní Fhloinn et al., 2014) found that students reported a positive impact of mathematics support on retention, confidence, performance and ability to cope with the mathematical demands of their courses. It is interesting to note that these studies rely on student selfreporting, and have not tracked individual student's progress with engagement in a support programme. A major challenge of support programmes is catering for diverse student needs (Jackson et al., 2014). In addition, online learning, such as can be experienced in a support programme, requires high motivation and selfregulated learning, and negative learning emotions form significant impediments to online learning (Tempelaar et al., 2012).
The present study is unique in two aspects: firstly, it focuses on mathematical skills in the context of a chemistry higher education first year cohort with diverse mathematical backgrounds and secondly, it incorporates usage tracking data from students who used a maths skills support programme. This study created a support programme for Maths Skills that was integrated in the first year chemistry curricula. In particular, we sought to understand;
• What are first year chemistry students’ perceptions towards Mathematics?
• What are students’ patterns of usage of a Maths Skills support programme integrated into first year chemistry?
• What is the relationship between students use of a Maths Skills support programme and their performance in first year chemistry?
Fig. 2 Admission requirements for Science degrees (n = 16) offered within Queensland in 2015. Double degrees, food science, environmental, medical or veterinary sciences degrees were excluded. 
In this study the dependent variables are the level of achievement and academic mathematical background of students, as well as the grade (Pass, Fail or numerical values of 1–7) and percentage marks that the students received for assessment items within the Chemistry course. Table 1 presents the correlation of the grades (and the numerical coding) with the percentage marks. The distribution of grades in the Chemistry course in 2014–2015 was typical for a first year course and previous offerings of the course.
Grade (numerical)  1–3  4  5  6  7 
Mark range (%)  0–49  50–64  65–74  75–84  85–100 
Grade descriptor  Fail (F)  Pass (P)  Credit (Cr)  Distinction (D)  High distinction (HD) 
Notes  Written and illustrated to explain topic clearly including many discipline worked examples, directly applied to chemistry 
Questions  Crossreferenced to notes and a range of simple to difficult questions 
Answers  Worked answers were provided to assist selfdirected learning and build confidence 
Online problems  Were available to provide further practice in an adaptive learning environment 
Fig. 3 Example of an instructive illustration from the Scientific Notation Notes section of the Maths Skills Site. 
The Questions were cross referenced to the notes and ranged in difficulty to scaffold skill development. An example from the “Logarithms and pH” section illustrates the use of simple and more challenging selfpaced questions (Fig. 4). Worked answers for every question were available to help build student confidence and provided selfpaced feedback on questions.
Fig. 4 Example of simple and more challenging questions from the logarithms and pH Note section of the Maths Skills Site. 
Links to Multiplechoice online questions that were chemistry based and required mathematical manipulations (sourced from the publisher's online database in the Chemistry textbook) were available to help build student confidence and enable the students to practice the appropriate mathematical skills, in a lowstress environment, until they have mastered the required skill and gained confidence.
Question  

a Refers to the level of achievement given by the Queensland Studies authority where VLA = very low achievement, LA = low achievement, SA = sound achievement, HA = high achievement and VHA = very high achievement. SA is required for University admission.  
Yr10
N (%) 
Yr11
N (%) 
Yr12
N (%) 
Other
N (%) 
None
N (%) 

1. What level of Chemistry did you successfully complete at School or later (e.g. TAFE)?  61(18)  15(4)  206(59)  13(4)  52(15) 
2. What level of Biology did you successfully complete at School or later?  57(16)  12(3)  215(62)  14(4)  48(14) 
None
N (%) 
Other
N (%) 
Maths A
N (%) 
Maths B
N (%) 
Maths C
N (%) 

3. What level of Maths did you successfully study at School in year 11?  5(1)  18(5)  61(18)  172(50)  88(26) 
4. What level of Maths did you successfully study at School in year 12?  6(2)  20(6)  87(25)  152(44)  80(23) 
VLA
N (%) 
LA
N (%) 
SA
N (%) 
HA
N (%) 
VHA
N (%) 

5. If you completed year 12 Maths A, what grade did you achieve? (VLA to VHA)^{a}  1(1)  1(1)  26(28)  39(42)  26(28) 
6. If you completed year 12 Maths B, what grade did you achieve?  1(1)  4(2)  75(32)  85(37)  66(29) 
7. If you completed year 12 Maths C, what grade did you achieve?  0(0)  1(1)  16(19)  28(33)  39(46) 
Yes
N (%) 
No
N (%) 

8. Did you do the Chemistry Bridging Course?  27(9)  306(91)  
9. Did you do the Maths bridging course?  17(5)  318(95)  
Not at all important
N (%) 
Not important
N (%) 
Neutral
N (%) 
Important
N (%) 
Very important
N (%) 

10. How important do you think Mathematics is for the study of Chemistry?  0(0)  9(3)  42(12)  169(49)  127(37) 
11. How important do you think Mathematics is for the study of Biology?  24(7)  95(28)  140(41)  69(20)  72(21) 
Not at all confident
N (%) 
Not confident
N (%) 
Neutral
N (%) 
Confident
N (%) 
Very confident
N (%) 

12. Rate your confidence in your current chemistry knowledge?  26(8)  56(16)  145(42)  94(27)  23(7) 
13. Rate your confidence in your mathematical skills?  14(4)  39(11)  135(39)  109(32)  48(14) 
In addition, the students who responded to the questionnaire selfidentified their achievement and academic background in chemistry, biology and mathematics, using the Queensland Studies Authority (QSA) levels of achievement (Fig. 1 caption). This was cross checked with the high school grades obtained from their admission records, where such data was available, and indicated that students were selfreporting their achievement and background correctly. Nonschool leavers also reported their prior studies and included the categories of other studies (not years 10, 11 or 12) or no study. School leaver respondents selfreported any participation in bridging courses for chemistry and/or mathematics. All data were deidentified and aggregated for reporting.
Question  

Strongly disagree
N (%) 
Disagree
N (%) 
Neutral
N (%) 
Agree
N (%) 
Strongly agree
N (%) 

1. I did not use the Maths Skills Site as I was unaware of the site linked to Chemistry 1A  4(13.8)  5(17.2)  3(10.3)  11(37.9)  6(20.7) 
2. I aware of the Maths Skills Site but did not feel I needed to use it  4(13.8)  6(20.7)  5(17.2)  8(27.6)  7(24.1) 
3. I did not use the Maths Skills Site as I did not have enough time during semester  3(10.3)  9(31.0)  11(37.9)  2(6.9)  1(3.4) 
4. I did not use the Maths Skills Site as it was not assessable for Chemistry  3(10.3)  13(44.8)  5(17.2)  5(17.2)  3(10.3) 
5. I did not use the Maths Skills Site as I was told not use it by others  10(34.5)  10(34.5)  4(13.8)  2(6.9)  3(10.3) 
6. After semester 1 my confidence in doing chemistry problems has increased  2(6.9)  0(0)  9(31.0)  11(37.9)  7(24.1) 
7. After semester 1 my confidence with mathematics has increased  2(6.9)  4(13.8)  12(41.4)  7(24.1)  4(13.8) 
8. Mathematics skills are important for the study of chemistry.  0(0)  0(0)  6(20.7)  9(31.0)  14(48.3) 
Never
N (%) 
Rarely
N (%) 
Sometimes
N (%) 
Regularly
N (%) 
Almost always
N (%) 

9. I feel anxious when I have to answer chemistry problems requiring calculations  7(24.1)  8(27.6)  8(27.6)  4(13.8)  2(6.9) 
Question  

Never
N (%) 
Rarely
N (%) 
Sometimes
N (%) 
Regularly
N (%) 
Almost always
N (%) 

1. I used or read the Maths Skills module notes  1(12.5)  0(0)  3(37.5)  2(25)  2(25) 
2. The Maths Skills module notes were helpful for my study of Chemistry  1(12.5)  0(0)  2(25)  4(50)  1(12.5) 
3. I attempted the problems in the Maths Skills modules.  1(12.5)  1(12.5)  0(0)  5(62.5)  1(12.5) 
4. The answer sheets in the Maths Skills module were useful  1(12.5)  0(0)  2(25)  4(50)  1(12.5) 
5. The Maths Skills module notes provided enough examples to understand problems in Chemistry  1(12.5)  0(0)  2(25)  3(37.5)  2(25) 
6. The Maths Skills module notes did not help me when solving chemistry problems  4(50)  1(12.5)  3(37.5)  0(0)  0(0) 
7. l feel anxious when I have to answer chemistry problems requiring calculations  1(12.5)  1(12.5)  3(37.5)  3(37.5)  0(0) 
Strongly disagree
N (%) 
Disagree
N (%) 
Neutral
N (%) 
Agree
N (%) 
Strongly agree
N (%) 

8. After using some/or all of the Maths Skills modules my confidence in doing chemistry problems has increased  1(12.5)  0(0)  2(25)  4(50)  1(12.5) 
9. My confidence with mathematics has increased  1(12.5)  0(0)  2(25)  4(50)  1(12.5) 
10. Overall I am satisfied with the maths skills modules  1(12.5)  0(0)  2(25)  4(50)  1(12.5) 
Students who progressed to second year chemistry were asked to voluntarily respond to a followup survey (∼ one year after completing the Chemistry course). Whilst only a small cohort (n = 13) of students responded, it nonetheless provided some insight into students’ perceptions and usage of the resource and suggested reasons why students were not using the extra maths support in first year chemistry.
We carried out a survey of the entry requirements on mathematics prerequisites for science programmes in Queensland (from QTAC Sciences section), as listed for entry by the Queensland Tertiary Admissions Centre for 2015 (Fig. 2). Of the 48 degrees listed, 56% had a maths prerequisite, 25% had combinations of maths priorassumed knowledge. Of concern, were nine science degrees (19%) that had no prior assumed or prerequisite maths knowledge needed for university entry. The students in this study were enrolled in a first year chemistry course that was offered in degree programmes with varying mathematical prerequisites and prior assumed entry requirements. A snapshot of the mathematical backgrounds of the 2014 subcohort has been reported previously (Loughlin et al., 2015). Success in formative and summative assessment within the chemistry course was enabled by prior study of Mathematics B or B/C in combination with chemistry prior knowledge (Loughlin et al., 2015).
We developed the MSS, (vide supra), in the context of the varied mathematical backgrounds and performance levels of students entering with Maths A, B or C or no year 12 mathematics. Consideration of the mathematical background of students guided the curriculum of the resource and resulted in the inclusion of topics ranging from elemental numeracy skills, such as positive and negative numbers and significant figures to more mathematical concepts such as algebra, simultaneous and quadratic equations.
Tracking of usage by individual students revealed that a typical usage was single onoff login to survey all topics (69% of users). The remaining students (31%) loggedin to the site 2–5 times during semester, accessing individual specific items (module notes, questions, etc.) anywhere between 18–120 times across the various Maths Skills topics. Aggregated access by students to the topic notes (Fig. 6) indicated the overall preferences, with the positive and negative numbers topic being the most accessed. We mapped the student usage (by single and multiple user) of topics against the chemistry curriculum; e.g. algebra and exponents were used in the energy and thermochemistry unit in weeks 7–8 of semester and areas such as positive/negative numbers were used more widely in the curriculum. It was noted that student usage of the topics in the MSS was variably distributed across the semester (c.f.Fig. 5a and b), and no correlation was observed with the timing of the chemistry curriculum.
Further analysis indicated students were individual in their choices within the site. This is illustrated by three examples of typical usage ‘types’ of the MSS resources:
• Student Usage Type A: Accessed all the notes, questions, and answers available on the topics of positive and negative numbers, significant figures, scientific notation and exponents, but did not access other topics, such as algebra.
• Students Usage Type B: Accessed all the notes for every topic, and the online multiplechoice questions, but did not access the selfinstruction questions and answers for any topic
• Student Usage Type C: Accessed the significant figures, scientific notation and graphing notes, and had a mixed approach to problems by accessing the online multiplechoice questions, and selectively choosing the significant figures selfinstruction questions and answers.
The survey of the students who completed the questionnaire but did not use the MSS (Table 4) indicated that the predominant reasons for nonuse was that students felt they did not need to use it (52%) or they were unaware of the site (59%) even though it was linked in the LMS to the Chemistry course. The followup survey of second year students indicated that students who did not use the site were ‘already confident’ with their own mathematics ability and had found alternative resources to study for the Mathematics needed for chemistry. Those who did use the site reported problems with the website lagging, which may be due to external factors, but also provided open ended responses about the Maths Skills Site: ‘helped with problems I came across’, ‘practice (was good)’ and ‘it helped me understand’.
The student's perceptions were identified from the questionnaire and followup surveys (research question 1). From the questionnaire data it is evident that students at the beginning of the semester realised the importance of mathematical skills to their science studies (both chemistry and biology), however, their confidence levels were low irrespective of their background. At the end of semester, the students who responded to the survey, felt more confident but there was still anxiety associated with mathematical calculations. Despite feeling anxious few students availed themselves of the online Maths Skills Site selfhelp resources although there was some increase in usage just before assessments were due.
Student patterns of usage for the site were identified through user statistics tracking within the LMS (research question 2). The ‘peak and trough’ pattern of usage of the resource by students was suggestive of ‘in the moment’ responses and a ‘justintime’ study for assessment mindset. The types of usage indicate that usage by type (notes, questions, answers, online problems) indicated a preferred usage by some students for the notes (suggestive of passive learning) and a preferred usage by other students for the multiplechoice online problems (suggestive of interactive learning). A selfdirected problem solving approach, through accessing the questions and answers sections, was poorly used by students, as compared to the usage of the notes and online problems. The usage preference of students who accessed the topic notes was towards scientific and numeracy skills, positive and negative numbers, significant figures, scientific notation and exponents (Fig. 6). Apart from algebra, the more challenging topics of logarithms, quadratic equations were less used; which is likely to be a reflection of the frequency of use of such topics in the chemistry curriculum. Further analysis of the usage indicated students were selecting topics and individual items (notes, questions, answers, online multiple choice questions) through a selfdirected approach where the student would tailor their own individual learning.
Correlation of the patterns of usage for the site with student final grades, albeit from a small sample, nonetheless suggest a positive relationship between the use of a Maths Skills support programme and student performance in first year chemistry (research question 3). It was interesting to note the distribution of grades was similar for users or nonusers of the MSS, with a peak occurring for the credit grade of 5 (Fig. 7). Users who accessed the MSS >40 times were more highly represented in the credit grade category. Although the academic outcomes for the students that used the MSS are distributed across the grades, it may be that the more motivated students are selfselecting to use the site.
High achieving students are intrinsically motivated as well as extrinsically (for example by a desire to earn a competitive place in graduate Medical School). The majority of tertiary students however appear to be extrinsically motivated by assessment stressors (Armstrong et al., 2013). The modularisation of units focuses students’ attention on end of semester exams and other summative assessments, and this fosters surface learning and memorisation (Armstrong et al., 2013). It does not allow integration to conceptual knowledge which takes time and a deeper approach. The problem therefore is how to motivate those students who most need extra help to adopt a deeper approach and make use of the online support provided. Research has shown that the learning strategies and selfefficacy of the students determines in part their success in an online developmental mathematics course (Wadsworth et al., 2007) and there is a positive correlation between selfassessment and academic performance (McDonald and Boud, 2003; Ibabe and Jauregizar, 2010). Interestingly, there is a negative correlation between students’ grades and their own estimation about their grades indicating a deficit in metacognitive skills (Vadhan and Stander, 1994). It has been suggested that we better train students in metacognitive capacities (Pintrich, 2002) and indeed learning strategies and selfefficacy can be developed (Weinstein et al., 2000). Thus it is recommended that systematic formative selfassessment activities are incorporated into the curriculum to improve students’ metacognitive skills (Ibabe and Jauregizar, 2010). In this way the use of selfhelp resources by those students who need them will increase and consequently their understanding of mathematics in context should improve. In addition, raising students’ awareness of their mathematical knowledge base through diagnostic testing has been trialled elsewhere (Kemp et al., 2011; Wilkes, 2015).
In conclusion, after a semester of study, the chemistry students who were surveyed had increased confidence with chemistry and mathematics, yet a significant proportion of students (37%) were still anxious when having to answer questions requiring calculations. The usage of the resources was varied. Students who were already confident with their abilities tended not to use the site. Students who accessed the site displayed improved achievements in the credit grade category, as compared to nonusers. They used a selfdirected approach, choosing to tailor their individual learning within the Maths Skills Site and did not correlate their usage of the site with the timing of the chemistry curriculum. Those who used the site were positive about the usefulness of the content (notes, questions, and answers) and the help provided for problem solving in Chemistry. However, the implementation of digital approaches to Maths Skills support requires smoother technological solutions. Significantly, this study indicated the facility for students to ‘tailor’ an individual approach to selfdirected learning assisted in students’ usage of mathematical skills support in chemistry, and apparently led to sound academic outcomes. Future studies will thus focus on the contextualisation of mathematical skills within scientific disciplines, such as biochemistry, and find ways to motivate the students to use the selfhelp resources and make the technology more efficient and engaging.
Now open the module folder, work through the notes, do the questions, and check your answers.
But does it really make sense to write down all the decimal places? Was the number of moles of solute measured accurately to the same number of decimal places? We need a rule to know how many decimal places to use when 'combining' two quantities (or two numbers). The answer is to use significant figures.
We want to calculate number of moles so we need to have by itself (only on one side of the equals sign and everything else on the other side). To do this, we need to use a very important rule for equations.
Whatever you do to one side of the equation, you MUST do to the other side of the equation
We are allowed to do anything we like to one side of an equation, as long as we do the exact same thing to the other side of the equation.
To leave n by itself, we need to ‘remove’ the divide by volume. But we can’t just ‘remove’ something from an equation just because we don’t want it there. Instead, we need to ‘move it to the other side’. As we are dividing by volume, we will multiply both sides of the equation by volume.
While this now looks different from our initial formula, we haven’t actually changed anything. By doing the exact same thing to both sides of the equation, we have not changed the formula, only the way the formula ‘looks’. On the right hand side, we can now cancel the volumes. (If you are unsure about cancelling, have a look back at the ‘Division in Algebra’ section in these notes.) End of extract from page 13 of algebra notes.
−5 + 3 = ? 
The first number is −5, so we start at −5 on the number line. It is addition, so we will be moving to the right. The second number is 3, so we will be moving 3 spaces.
(a) [H+] = 0.058 M
(b) [H+] = 0.0004 M
(c) [H+ ] = 4.5 × 10^{−6} M
(d) [H+] = 8.2 × 10^{−4} M
(Question 1) x^{2} − 3x + 2 = 0
(Question 2) x^{2} − 2x − 3 = 0
………
HSO_{4}^{−}(aq) + H_{2}O(l) ⇌ H_{3}O^{+}(aq) + SO_{4}^{2−}(aq) 
Initially the concentration of HSO_{4}^{−} was 0.50 M, the initial concentration of H_{3}O^{+} was 0.02 and the initial concentration of SO_{4}^{2−} was 0.08 M.
x + y = 5 
4x + 2y = 14 
(a) 5.24 × 10^{3}; (b) 5.241 × 10^{3}; (c) 0.52 × 10^{4}; (d) 5.241 × 10^{3}.
This journal is © The Royal Society of Chemistry 2016 