Question

a balloon holds 31.7 kg of helium. what is the volume of the balloon if the pressure is 1 atm and the temperature is 24°c? l

Explanation:

Step1: Calculate the number of moles of helium

The molar mass of helium (\(M = 4\space g/mol\)). The mass of helium \(m=31.7\space kg = 31700\space g\).
The number of moles \(n=\frac{m}{M}\)
\(n=\frac{31700\space g}{4\space g/mol}=7925\space mol\)

Step2: Convert the temperature to Kelvin

The temperature \(T = 24^{\circ}C\). Using the conversion \(T(K)=T(^{\circ}C)+ 273.15\)
\(T=(24 + 273.15)K=297.15K\)

Step3: Apply the ideal gas law \(PV=nRT\)

We know that \(P = 1\space atm\), \(R=0.0821\space L\cdot atm/(mol\cdot K)\), \(n = 7925\space mol\), \(T=297.15K\)
From \(V=\frac{nRT}{P}\)
\(V=\frac{7925\space mol\times0.0821\space L\cdot atm/(mol\cdot K)\times297.15K}{1\space atm}\)
First, calculate \(7925\times0.0821 = 650.6425\)
Then \(650.6425\times297.15=193338.42\)

Answer:

\(193338.42L\)