Question

A $\to$ P, is a zero-order reaction. At 300 K, this reaction was started with [A]=0.5 mol L$^{-1}$. After 100 s, the concentration of A was 0.05 mol L$^{-1}$. What is the rate constant (in mol L$^{-1}$s$^{-1}$) of this reaction?

• A. $2.303\times10^{-2}$
• B. $2.303\times10^{-3}$
• C. $4.5\times10^{-2}$
• D. $4.5\times10^{-3}$

Hint:

Zero-order: [A]$_t$ = [A]$_0$ - $k t$. Rate constant units are mol L$^{-1}$ s$^{-1}$. Solve linearly for $k$. Verify concentration and time units.

Answer 1

The Correct Option is D

1. For a zero-order reaction, [A]$_t$ = [A]$_0$ - $k t$, where $k$ is the rate constant.
2. Given [A]$_0$ = 0.5 mol L$^{-1}$, [A]$_t$ = 0.05 mol L$^{-1}$, $t$ = 100 s.
3. Substitute: $0.05 = 0.5 - k \times 100$.
4. Solve: $k \times 100 = 0.5 - 0.05 = 0.45$, so $k = 0.45 / 100 = 0.0045 = 4.5 \times 10^{-3}$ mol L$^{-1}$ s$^{-1}$.
5. Thus, the answer is (4) $4.5\times10^{-3}$.