Question

choose the correct set of variables to solve the following problem: what is the volume of a balloon if it contains 3.2 moles of helium at a temperature of 20°c and 1.2 atm?
p = 293 k, v = 3.2 mol, n = x (unknown), t = 1.2 atm
p = x (unknown), v = 3.2 mol, n = 1.2 atm, t = 20°c k
p = 1.2 atm, v = 3.2 mol, n = 20°c, t = x (unknown)
p = 1.2 atm, v = x (unknown), n = 3.2 mol, t = 293 k

Explanation:

Step1: Recall the ideal gas law

The ideal gas law is \(PV = nRT\). We need to find \(V\), so we can rearrange the formula to \(V=\frac{nRT}{P}\).

Step2: Identify the values

Given \(n = 3.2\space mol\), \(R = 0.0821\space L\cdot atm/(mol\cdot K)\) (gas constant), \(T=20^{\circ}C=(20 + 273)K=293K\), \(P = 1.2\space atm\).

Step3: Substitute the values into the formula

\(V=\frac{3.2\times0.0821\times293}{1.2}\).
First, calculate \(3.2\times0.0821\times293\):
\(3.2\times0.0821 = 0.26272\), then \(0.26272\times293=77.077\).
Then divide by \(1.2\): \(V=\frac{77.077}{1.2}=64.23\space L\).

Answer:

The fourth option (\(P = 1.2\space atm\), \(V=x\) (unknown), \(n = 3.2\space mol\), \(T = 293\space K\)) is the correct set of variables.