Applied Calculus in Chemistry Quiz

1. For a reaction [A](t) = 3e^(-0.08t) mol/L, what is the reaction rate at t = 5 s?

a) -0.24e^(-0.4) mol/L/s

b) -3e^(-0.08) mol/L/s

c) -0.08 mol/L/s

d) -3 mol/L/s

2. What is the half-life of a reactant [A](t) = 4e^(-0.05t)?

a) ln(2)/0.05 seconds

b) ln(4)/0.05 seconds

c) 0.05 seconds

d) ln(2) seconds

3. True or False: The rate of a chemical reaction depends on the derivative of concentration.

a) True

b) False

4. For a second-order reaction 1/[A] = 0.2t + 1, what is d[A]/dt at t = 2?

a) -0.08/(1.4)² mol/L/s

b) -0.2 mol/L/s

c) -1.4 mol/L/s

d) -0.08 mol/L/s

5. What is the rate of heat flow Q(t) = 500(1 - e^(-0.1t)) J at t = 3?

a) 50e^(-0.3) J/s

b) 500e^(-0.1) J/s

c) 50 J/s

d) 500 J/s

6. For Gibbs free energy G(T) = -100T + 0.5T², what is dG/dT at T = 300 K?

a) 200 J/K

b) -100 J/K

c) 300 J/K

d) 0 J/K

7. What is the total amount of product formed from t = 0 to t = 10 if d[P]/dt = 0.02 mol/s?

a) 0.2 mol

b) 0.02 mol

c) 2 mol

d) 10 mol

8. True or False: Calculus is used to calculate equilibrium constants.

a) True

b) False

9. For a gas expansion P(V) = 1000/V Pa, what is dP/dV at V = 2 m³?

a) -250 Pa/m³

b) -1000 Pa/m³

c) 250 Pa/m³

d) 500 Pa/m³

10. What is the entropy change ΔS = ∫[300,400] (50/T) dT J/K?

a) 50 ln(400/300) J/K

b) 50 J/K

c) 400/300 J/K

d) 50 * 100 J/K