For the reaction A(g) + 1/2 B(g) → 2 C(g): b. When C is increasing at a rate of 0.025 M/s, how fast is B decreasing? How fast is A decreasing? a. Determine the expression for the rate of the reaction in terms of the change in concentration of each of the reactants and products.

Verified step by step guidance

1. <insert step 1> Start by writing the general rate expression for the reaction: \( \text{Rate} = -\frac{1}{a} \frac{\Delta [A]}{\Delta t} = -\frac{1}{b} \frac{\Delta [B]}{\Delta t} = \frac{1}{c} \frac{\Delta [C]}{\Delta t} \), where \( a, b, \) and \( c \) are the stoichiometric coefficients of A, B, and C respectively.>
2. <insert step 2> For the given reaction \( A(g) + \frac{1}{2} B(g) \rightarrow 2 C(g) \), identify the stoichiometric coefficients: \( a = 1 \), \( b = \frac{1}{2} \), and \( c = 2 \).>
3. <insert step 3> Substitute the stoichiometric coefficients into the rate expression: \( \text{Rate} = -\frac{1}{1} \frac{\Delta [A]}{\Delta t} = -\frac{1}{\frac{1}{2}} \frac{\Delta [B]}{\Delta t} = \frac{1}{2} \frac{\Delta [C]}{\Delta t} \).>
4. <insert step 4> Given that \( \frac{\Delta [C]}{\Delta t} = 0.025 \text{ M/s} \), use the rate expression \( \frac{1}{2} \frac{\Delta [C]}{\Delta t} = -\frac{1}{\frac{1}{2}} \frac{\Delta [B]}{\Delta t} \) to find the rate at which B is decreasing.>
5. <insert step 5> Similarly, use the rate expression \( \frac{1}{2} \frac{\Delta [C]}{\Delta t} = -\frac{1}{1} \frac{\Delta [A]}{\Delta t} \) to find the rate at which A is decreasing.>