Question

taken ap chem 2017 free-response questions answers: (a) 0.31 mol cl₂ and (b) 7.9 g cs₂

cs₂(g) + 3 cl₂(g) → ccl₄(g) + s₂cl₂(g)

1. carbon tetrachloride, ccl₄(g), can be synthesized according to the reaction represented above. a chemist runs the reaction at a constant temperature of 120°c in a rigid 25.0 l container.

(a) chlorine gas, cl₂(g), is initially present in the container at a pressure of 0.40 atm.

(i) how many moles of cl₂(g) are in the container?

(ii) how many grams of carbon disulfide, cs₂(g), are needed to react completely with the cl₂(g) ?

hint: pv = nrt r= 0.08206 l atm / mol k ; n = pv / rt

Explanation:

Part (a)(i)

Step1: Convert temperature to Kelvin

The temperature is \(120^\circ\text{C}\), so \(T = 120 + 273.15 = 393.15\,\text{K}\).

Step2: Use ideal gas law \(n=\frac{PV}{RT}\)

Given \(P = 0.40\,\text{atm}\), \(V = 25.0\,\text{L}\), \(R = 0.08206\,\text{L atm/mol K}\), \(T = 393.15\,\text{K}\).
\[
n=\frac{0.40\,\text{atm} \times 25.0\,\text{L}}{0.08206\,\text{L atm/mol K} \times 393.15\,\text{K}}
\]
Calculate numerator: \(0.40\times25.0 = 10.0\)
Denominator: \(0.08206\times393.15\approx32.26\)
\[
n\approx\frac{10.0}{32.26}\approx0.31\,\text{mol}
\]

Step1: Determine mole ratio from reaction

Reaction: \(\text{CS}_2(g) + 3\text{Cl}_2(g)
ightarrow\text{CCl}_4(g) + \text{S}_2\text{Cl}_2(g)\). Mole ratio of \(\text{CS}_2\) to \(\text{Cl}_2\) is \(1:3\).
Moles of \(\text{Cl}_2 = 0.31\,\text{mol}\), so moles of \(\text{CS}_2 = \frac{0.31\,\text{mol}}{3}\approx0.1033\,\text{mol}\).

Step2: Calculate molar mass of \(\text{CS}_2\)

Molar mass of \(\text{C} = 12.01\,\text{g/mol}\), \(\text{S} = 32.07\,\text{g/mol}\).
\[
\text{Molar mass of } \text{CS}_2 = 12.01 + 2\times32.07 = 76.15\,\text{g/mol}
\]

Step3: Calculate mass of \(\text{CS}_2\)

\[
\text{Mass} = \text{moles} \times \text{molar mass} = 0.1033\,\text{mol} \times 76.15\,\text{g/mol}\approx7.9\,\text{g}
\]

Answer:

\(0.31\,\text{mol}\)

Part (a)(ii)