भौतिक रसायन

For a first order reaction, the relationship between rate constant ($k$) and half-life ($t_{1/2}$) is:

Given $t_{1/2} = 25\text{ min}$:

Calculation steps:

• Find initial concentration of $\text{H}^+$ ions:
  Volume $V = 0.05\text{ mL} = 0.05 \times 10^{-3}\text{ L} = 5 \times 10^{-5}\text{ L}$.
  $[\text{H}^+]_0 = \frac{\text{Moles}}{\text{Volume in L}} = \frac{3.0 \times 10^{-9}\text{ mol}}{5 \times 10^{-5}\text{ L}} = 6.0 \times 10^{-5}\text{ mol L}^{-1}$.
• The units of the rate constant are $\text{mol L}^{-1}\text{ s}^{-1}$, indicating a zero order process where rate $= k$.
• Time required for complete disappearance ($[\text{H}^+] = 0$):
  $$t = \frac{[\text{H}^+]_0}{k} = \frac{6.0 \times 10^{-5}\text{ mol L}^{-1}}{1.0 \times 10^{-7}\text{ mol L}^{-1}\text{ s}^{-1}} = 600\text{ s} = 6 \times 10^2\text{ s}$$

Analysis of statements regarding order of reaction:

• By definition, order is the sum of the powers of concentrations in the rate law expression (correct).
• Order cannot be predicted directly from the stoichiometric coefficients of a balanced equation for complex/multi-step reactions; it is only equal to stoichiometric coefficients for simple elementary steps. Therefore, stating that order is 'always equal' to the sum of stoichiometric coefficients is incorrect.
• The order of a reaction can be zero, integral, or fractional (correct).
• The order of a reaction is strictly an experimentally determined quantity (correct).