SEMI FINAL STAGE 2026
Mfantsipim School: 56 points
Presbyterian Boys' Sec. Sch: 53 points
Osei Tutu SHS: 27 points
QUESTION
The rate law for a reaction between reactants A and B is given by $R=k[\text{A}]^2[\text{B}]^3$.
What is the rate constant and its units for a reaction in which
$[\text{A}] = [\text{B}]$
$[\text{A}] = 0.200$
mol/dm³, and the rate is $2.00\times10^{-4}$ mol/dm³/s?
NOTE: In a rate law, $k$ is the rate constant, a kinetics quantity, not an equilibrium constant.
The number/units below answer what was actually asked.
ANSWER: $k=6.25\times10^{-1}$ mol$^{-4}$dm$^{12}$s$^{-1}$
SOLUTION:
$k = \dfrac{R}{[\text{A}]^2[\text{B}]^3}$
$k = \dfrac{2.00\times10^{-4}}{(0.200)^2(0.200)^3}$
$k = \dfrac{2.00\times10^{-4}}{(0.200)^5}$
$(0.200)^5=3.2\times10^{-4}$, so
$k = \dfrac{2.00\times10^{-4}}{3.2\times10^{-4}}$
$k = \dfrac{2\times10^{-4}}{32\times10^{-5}}$
$k = \dfrac{1}{16} \times10^{1}$
$k = 0.625$
$k = 6.25\times10^{-1}$
Units shortcut: for overall order $n$ (here
$n = 2+3$
$n = 5$
), $k$'s units are always mol$^{1-n}$dm$^{3(n-1)}$s$^{-1}$.
With $n=5$: mol$^{-4}$dm$^{12}$s$^{-1}$.
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PRACTICE QUESTIONS
1. QUESTION: The rate law for a reaction is $R=k[\text{A}][\text{B}]^2$. What is the rate constant and its units when [A] = [B] = 0.100 mol/dm³ and the rate is $2.00\times10^{-5}$ mol/dm³/s?
ANSWER: $k = 2.00\times10^{-2}$ mol⁻² dm⁶ s⁻¹
SOLUTION:
$k = \dfrac{R}{[\text{A}][\text{B}]^2}$
$k = \dfrac{2.00\times10^{-5}}{1.00\times10^{-3}}$
$k = \dfrac{2\times10^{-5}}{10^{-3}}$
$k = 2.00\times10^{-2}$
Units: mol⁻² dm⁶ s⁻¹
2. QUESTION: The rate law for a reaction is $R=k[\text{A}]^2$. What is the rate constant and its units when [A] = 0.300 mol/dm³ and the rate is $4.50\times10^{-3}$ mol/dm³/s?
ANSWER: $k = 5.00\times10^{-2}$ dm³ mol⁻¹ s⁻¹
SOLUTION:
$k = \dfrac{R}{[\text{A}]^2}$
$k = \dfrac{4.50\times10^{-3}}{9.00\times10^{-2}}$
$k = \dfrac{45\times10^{-4}}{9\times10^{-2}}$
$k = 5.00\times10^{-2}$
Units: dm³ mol⁻¹ s⁻¹
3. QUESTION: The rate law for a reaction is $R=k[\text{A}]^2[\text{B}]$. What is the rate constant and its units when [A] = [B] = 0.200 mol/dm³ and the rate is $1.20\times10^{-3}$ mol/dm³/s?
ANSWER: $k = 0.150$ mol⁻² dm⁶ s⁻¹
SOLUTION:
$k = \dfrac{R}{[\text{A}]^2[\text{B}]}$
$k = \dfrac{1.20\times10^{-3}}{8.00\times10^{-3}}$
$k = \dfrac{12\times10^{-4}}{8\times10^{-3}}$
$k = \dfrac{3}{2} \times10^{-1}$
$k = 0.150$
Units: mol⁻² dm⁶ s⁻¹
4. QUESTION: The rate law for a reaction is $R=k[\text{A}][\text{B}]$. What is the rate constant and its units when [A] = [B] = 0.200 mol/dm³ and the rate is $8.00\times10^{-4}$ mol/dm³/s?
ANSWER: $k = 2.00\times10^{-2}$ dm³ mol⁻¹ s⁻¹
SOLUTION:
$k = \dfrac{R}{[\text{A}][\text{B}]}$
$k = \dfrac{8.00\times10^{-4}}{4.00\times10^{-2}}$
$k = \dfrac{8\times10^{-4}}{4\times10^{-2}}$
$k = 2.00\times10^{-2}$
Units: dm³ mol⁻¹ s⁻¹
5. QUESTION: The rate law for a reaction is $R=k[\text{A}]$. What is the rate constant and its units when [A] = 0.250 mol/dm³ and the rate is $7.50\times10^{-3}$ mol/dm³/s?
ANSWER: $k = 3.00\times10^{-2}$ s⁻¹
SOLUTION:
$k = \dfrac{R}{[\text{A}]}$
$k = \dfrac{7.50\times10^{-3}}{0.250}$
$k = \dfrac{75\times10^{-4}}{25\times10^{-2}}$
$k = 3.00\times10^{-2}$
Units: s⁻¹
6. QUESTION: The rate law for a reaction is $R=k[\text{A}]^2[\text{B}]$. What is the rate constant and its units when [A] = [B] = 0.100 mol/dm³ and the rate is $3.00\times10^{-4}$ mol/dm³/s?
ANSWER: $k = 0.300$ mol⁻² dm⁶ s⁻¹
SOLUTION:
$k = \dfrac{R}{[\text{A}]^2[\text{B}]}$
$k = \dfrac{3.00\times10^{-4}}{1.00\times10^{-3}}$
$k = \dfrac{3\times10^{-4}}{10^{-3}}$
$k = 0.300$
Units: mol⁻² dm⁶ s⁻¹