Given the following data for the decomposition of H3PO4:Time (s): 10.0, 40.0Concentration of H3PO4 (mol/L): 0.200, 0.140What is the average rate of decomposition of H3PO4 between 10.0 s and 40.0 s?(Average rate = -Δ[H3PO4]/Δt)

• A. 1.67 × 10^{-3} mol L^{-1} s^{-1}
• B. 2.00 × 10^{-3} mol L^{-1} s^{-1}
• C. 6.00 × 10^{-3} mol L^{-1} s^{-1}
• D. 4.00 × 10^{-3} mol L^{-1} s^{-1}

Answer: (B)

Verified step by step guidance

1. Identify the initial and final concentrations of H3PO4 and the corresponding times. Here, the initial concentration \( [\mathrm{H_3PO_4}]_i = 0.200 \ \mathrm{mol/L} \) at time \( t_i = 10.0 \ \mathrm{s} \), and the final concentration \( [\mathrm{H_3PO_4}]_f = 0.140 \ \mathrm{mol/L} \) at time \( t_f = 40.0 \ \mathrm{s} \).
2. Calculate the change in concentration \( \Delta [\mathrm{H_3PO_4}] \) by subtracting the final concentration from the initial concentration: \( \Delta [\mathrm{H_3PO_4}] = [\mathrm{H_3PO_4}]_f - [\mathrm{H_3PO_4}]_i \).
3. Calculate the change in time \( \Delta t \) by subtracting the initial time from the final time: \( \Delta t = t_f - t_i \).
4. Use the formula for the average rate of decomposition: \[ \text{Average rate} = -\frac{\Delta [\mathrm{H_3PO_4}]}{\Delta t} \] Substitute the values of \( \Delta [\mathrm{H_3PO_4}] \) and \( \Delta t \) into this equation.
5. Perform the division to find the average rate of decomposition in units of \( \mathrm{mol \ L^{-1} \ s^{-1}} \). Remember the negative sign ensures the rate is positive since the concentration decreases over time.