Questions: Name: CHEM 111 Quiz 3 1) Given the reaction 2 A(g) -> B(g) + C(g) a) Express the rate of reaction in terms of the change in concentration in terms of the change in concentration of each of the reactants and products. b) When [C] is increasing at 2.0 mol / L s, how fast is [A] decreasing?

Solution Steps

For the reaction \(2 A_{(\mathrm{g})} \rightarrow B_{(\mathrm{g})} + \mathrm{C}_{(\mathrm{g})}\), the rate of reaction can be expressed in terms of the change in concentration of each reactant and product.

The rate of reaction \(r\) is given by: \[ r = -\frac{1}{2} \frac{d[A]}{dt} = \frac{d[B]}{dt} = \frac{d[C]}{dt} \]

Given that \([C]\) is increasing at \(2.0 \, \mathrm{mol/L \cdot s}\), we can use the rate expression to find how fast \([A]\) is decreasing.

From the rate expression: \[ r = \frac{d[C]}{dt} = 2.0 \, \mathrm{mol/L \cdot s} \]

Since: \[ r = -\frac{1}{2} \frac{d[A]}{dt} \]

We can set the rates equal to each other: \[ 2.0 = -\frac{1}{2} \frac{d[A]}{dt} \]

Solving for \(\frac{d[A]}{dt}\): \[ 2.0 = -\frac{1}{2} \frac{d[A]}{dt} \]

Multiply both sides by \(-2\): \[ \frac{d[A]}{dt} = -4.0 \, \mathrm{mol/L \cdot s} \]

Final Answer