Import Question JSON

« Back to Question List Edit Question »

Current Question (ID: 18283)

Question:
$\text{In a reaction between A and B, the initial rate of reaction (} r_0 \text{) was measured for different initial concentrations of A and B as given below:}$ $\begin{array}{ccc} \text{A / mol L}^{-1} & 0.20 & 0.20 & 0.40 \\ \text{B / mol L}^{-1} & 0.30 & 0.10 & 0.05 \\ r_0 / \text{mol L}^{-1} \text{s}^{-1} & 5.07 \times 10^{-5} & 5.07 \times 10^{-5} & 1.43 \times 10^{-4} \end{array}$ $\text{The order of the reaction with respect to A and B would be:}$
Options:
  • 1. $\text{The order with respect to A is 0.5 and with respect to B is zero}$
  • 2. $\text{The order with respect to A is 1 and with respect to B is 0.5}$
  • 3. $\text{The order with respect to A is 2 and with respect to B is 1}$
  • 4. $\text{The order with respect to A is 1.5 and with respect to B is zero}$
Solution:
$\text{HINT: The rate law is } R = k[\text{A}]^x[\text{B}]^y$ $\text{Step 1: Let the order of the reaction with respect to A be } x \text{ and with respect to B be } y.$ $5.07 \times 10^{-5} = k[0.20]^x[0.30]^y \quad (i)$ $5.07 \times 10^{-5} = k[0.20]^x[0.10]^y \quad (ii)$ $1.43 \times 10^{-4} = k[0.40]^x[0.05]^y \quad (iii)$ $\text{Dividing equation (i) by (ii), we obtain}$ $\frac{5.07 \times 10^{-5}}{5.07 \times 10^{-5}} = \frac{k[0.20]^x[0.30]^y}{k[0.20]^x[0.10]^y}$ $\Rightarrow 1 = \left(\frac{0.30}{0.10}\right)^y$ $\Rightarrow y = 0$ $\text{Step 2:}$ $\text{Calculate the order of the reaction with respect to A as follows}$ $\text{Dividing equation (iii) by (ii), we obtain}$ $\frac{1.43 \times 10^{-4}}{5.07 \times 10^{-5}} = \frac{k[0.40]^x[0.05]^y}{k[0.20]^x[0.30]^y}$ $\frac{1.43 \times 10^{-4}}{5.07 \times 10^{-5}} = \left(\frac{0.40}{0.20}\right)^x \left(\frac{0.05}{0.30}\right)^0$ $2.821 = 2^x$ $\Rightarrow \log 2.821 = x \log 2 \quad (\text{Taking log both sides})$ $x = \frac{\log 2.821}{\log 2}$ $= 1.496$ $= 1.5 \text{ (approximately)}$ $\text{Hence, the order w.r.t A is 1.5 and w.r.t B is zero.}$

Import JSON File

Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

Expected JSON Format:

{
  "question": "The mass of carbon present in 0.5 mole of $\\mathrm{K}_4[\\mathrm{Fe(CN)}_6]$ is:",
  "options": [
    {
      "id": 1,
      "text": "1.8 g"
    },
    {
      "id": 2,
      "text": "18 g"
    },
    {
      "id": 3,
      "text": "3.6 g"
    },
    {
      "id": 4,
      "text": "36 g"
    }
  ],
  "solution": "\\begin{align}\n&\\text{Hint: Mole concept}\\\\\n&1 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\text{ moles of carbon atom}\\\\\n&0.5 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\times 0.5 \\text{ mol} = 3 \\text{ mol}\\\\\n&1 \\text{ mol of carbon} = 12 \\text{ g}\\\\\n&3 \\text{ mol carbon} = 12 \\times 3 = 36 \\text{ g}\\\\\n&\\text{Hence, 36 g mass of carbon present in 0.5 mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6].\n\\end{align}",
  "correct_answer": 4
}