Question

a mixture of 1.00 g h₂ and 1.50 g he is placed in a 1.00 - l container at 28°c. calculate the partial pressure of each gas and the total pressure.

pr₂ = atm

pr = atm

ptotal = atm

3 item attempts remaining

Explanation:

Step1: Calculate the number of moles of each gas

• For \(H_2\):

The molar mass of \(H_2\) is \(M_{H_2}=2\space g/mol\). Using the formula \(n=\frac{m}{M}\), where \(m = 1.00\space g\) and \(M = 2\space g/mol\), we have \(n_{H_2}=\frac{1.00\space g}{2\space g/mol}=0.5\space mol\).

• For \(He\):

The molar mass of \(He\) is \(M_{He}=4\space g/mol\). Using the formula \(n=\frac{m}{M}\), where \(m = 1.50\space g\) and \(M = 4\space g/mol\), we have \(n_{He}=\frac{1.50\space g}{4\space g/mol}=0.375\space mol\).

Step2: Convert the temperature to Kelvin

Using the formula \(T=(t + 273.15)\space K\), where \(t = 28^{\circ}C\), we get \(T=(28+ 273.15)\space K=301.15\space K\). The volume \(V = 1.00\space L=1.00\times10^{- 3}\space m^{3}\).

Step3: Calculate the partial pressure of each gas using the ideal gas law \(P=\frac{nRT}{V}\)

• For \(H_2\):

\(R = 8.314\space J/(mol\cdot K)\). Substituting \(n = 0.5\space mol\), \(R = 8.314\space J/(mol\cdot K)\), \(T = 301.15\space K\) and \(V = 1.00\times10^{-3}\space m^{3}\) into \(P=\frac{nRT}{V}\), we have \(P_{H_2}=\frac{0.5\times8.314\times301.15}{1.00\times10^{-3}}\space Pa\). Converting to atm (\(1\space atm = 101325\space Pa\)), \(P_{H_2}=\frac{0.5\times8.314\times301.15}{1.00\times10^{-3}\times101325}\space atm\approx12.3\space atm\).

• For \(He\):

Substituting \(n = 0.375\space mol\), \(R = 8.314\space J/(mol\cdot K)\), \(T = 301.15\space K\) and \(V = 1.00\times10^{-3}\space m^{3}\) into \(P=\frac{nRT}{V}\), we have \(P_{He}=\frac{0.375\times8.314\times301.15}{1.00\times10^{-3}}\space Pa\). Converting to atm (\(1\space atm = 101325\space Pa\)), \(P_{He}=\frac{0.375\times8.314\times301.15}{1.00\times10^{-3}\times101325}\space atm\approx9.23\space atm\).

Step4: Calculate the total pressure using Dalton's law \(P_{total}=P_{H_2}+P_{He}\)

\(P_{total}=12.3 + 9.23=21.5\space atm\).

Answer:

\(P_{H_2}\approx12.3\space atm\), \(P_{He}\approx9.23\space atm\), \(P_{total}=21.5\space atm\)