General Chemistry II: Mathematics Reassessment

IntoChemistry | General Chemistry II Math Readiness

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Readiness reassessment

After targeted review, use these 24 different questions to check progress on the same six math skills.

Suggested: review any skill area below 75%; this cutoff is an instructional choice, not a validated prediction threshold. Scores are not automatically sent to Talon.

Choose one response for each question, then select “Check my answers.” No timer. Hints are optional. You can retry freely. Questions are formative, not proctored.

Question 1. Solve x² -8x + 15 = 0. What is the smaller root?

5 6 2 3

Hint for question 1

Two algebraic roots may exist; compare them.

Question 2. Solve x² -10x + 24 = 0. What is the smaller root?

6 3 4 7

Hint for question 2

Two algebraic roots may exist; compare them.

Question 3. Find pH when [H₃O⁺] = 1.0 × 10^-4 M.

6.00 5.00 3.00 4.00

Hint for question 3

The negative sign makes pH positive for concentrations below 1 M.

Question 4. Find pH when [H₃O⁺] = 1.0 × 10^-5 M.

6.00 7.00 4.00 5.00

Hint for question 4

The negative sign makes pH positive for concentrations below 1 M.

Question 5. A first-order quantity halves with k = 0.05 min⁻¹. Calculate half-life.

27.7 min 6.02 min 13.9 min 6.93 min

Hint for question 5

Use natural logarithm for exponential decay.

Question 6. A first-order quantity halves with k = 0.08 min⁻¹. Calculate half-life.

17.3 min 8.66 min 3.76 min 4.33 min

Hint for question 6

Use natural logarithm for exponential decay.

Question 7. A graph of ln[A] versus time has slope -0.05 s⁻¹. What is first-order k?

0.05 s⁻¹ 0.12 s⁻¹ 0.10 s⁻¹ 0.03 s⁻¹

Hint for question 7

The slope is negative but k is positive.

Question 8. A graph of ln[A] versus time has slope -0.3 s⁻¹. What is first-order k?

0.37 s⁻¹ 0.30 s⁻¹ 0.60 s⁻¹ 0.15 s⁻¹

Hint for question 8

The slope is negative but k is positive.

Question 9. 0.4 mol solute is dissolved in 2 kg of solvent. Find molality.

2 mol/kg 0.4 mol/kg 0.2 mol/kg 0.1 mol/kg

Hint for question 9

Molality has kilograms of solvent in the denominator.

Question 10. 0.5 mol solute is dissolved in 2.5 kg of solvent. Find molality.

0.1 mol/kg 0.4 mol/kg 2 mol/kg 0.2 mol/kg

Hint for question 10

Molality has kilograms of solvent in the denominator.

Question 11. An ICE-table approximation neglects x=0.01 M relative to C=0.4 M. What is 100x/C?

5.00 % 1.25 % 4.50 % 2.50 %

Hint for question 11

Compute change divided by initial concentration.

Question 12. An ICE-table approximation neglects x=0.015 M relative to C=0.5 M. What is 100x/C?

3.00 % 1.50 % 6.00 % 5.00 %

Hint for question 12

Compute change divided by initial concentration.

Question 13. An ICE-table variable must satisfy 0≤x≤0.20 M. Which root is physically allowed?

0.05 M 0.25 M −0.05 M −0.25 M

Hint for question 13

Check the physical bounds in addition to the algebra.

Question 14. What is the discriminant of x²−6x+5=0?

36 16 4 20

Hint for question 14

Use b²−4ac, including the sign of b.

Question 15. If pH=4.00, what is [H₃O⁺]?

1.0×10⁻⁴ M 4.0×10⁻⁴ M 1.0×10⁴ M 4.0×10⁻¹ M

Hint for question 15

Use the inverse operation of base-10 log.

Question 16. Increasing [H₃O⁺] tenfold changes pH by how much?

Increases by 1 Decreases by 10 Decreases by 1 Increases by 10

Hint for question 16

Think logarithmically, not linearly.

Question 17. A first-order sample starts at 80 mg and has passed two half-lives. How much remains?

20 mg 60 mg 10 mg 40 mg

Hint for question 17

Each half-life changes the remaining amount, not the original amount.

Question 18. What is e⁰?

0 e 1 10

Hint for question 18

Consider the exponent rule for zero.

Question 19. If a line rises by 6 units while x increases by 3 units, what is slope?

18 6 2 3

Hint for question 19

Use vertical change divided by horizontal change.

Question 20. For y=mx+b, what does b represent?

slope y-intercept curvature x-intercept

Hint for question 20

Substitute x=0 into the equation.

Question 21. For a mixture with 2 mol A and 3 mol B, what is mole fraction of A?

0.40 0.67 0.60 2.50

Hint for question 21

Divide the component moles by total moles.

Question 22. What is the molality of 1.0 mol solute in 500 g of solvent?

500 mol/kg 0.50 mol/kg 2.0 mol/kg 1.0 mol/kg

Hint for question 22

Convert solvent mass to kilograms.

Question 23. Using the conventional 5% check, does x=0.015 M satisfy small-x for C=0.10 M?

No; change is 150% Yes; change is 1.5% Yes; change is 0.15% No; change is 15%

Hint for question 23

Calculate percent before deciding.

Question 24. Which expression measures relative error compared with an accepted value?

accepted/measured × 100% measured/accepted × 100% (measured+accepted)/2 |measured−accepted|/|accepted| × 100%

Hint for question 24

Compare the difference with the reference quantity.

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