Question

1. a 1.20 g sample of dry ice is added to a 755 ml flask containing nitrogen gas at a temperature of 25.0°c and a pressure of 725 torr. the dry ice sublimes (converts from solid to gas) and the mixture returns to 25.0°c. what is the total pressure in the flask?

Explanation:

Step1: Calculate the number of moles of \(CO_2\)

The molar mass of \(CO_2\) is \(M = 44.01\space g/mol\).
Using the formula \(n=\frac{m}{M}\), where \(m = 1.20\space g\)
\(n_{CO_2}=\frac{1.20\space g}{44.01\space g/mol}\approx0.0273\space mol\)

Step2: Use the ideal gas law to find the pressure of \(CO_2\)

The ideal gas law is \(PV = nRT\).
First, convert the volume \(V = 755\space mL=0.755\space L\), temperature \(T=(25.0 + 273.15)K = 298.15\space K\), and \(R = 62.36\space L\cdot Torr/mol\cdot K\)
From \(P=\frac{nRT}{V}\), substitute \(n = 0.0273\space mol\), \(R = 62.36\space L\cdot Torr/mol\cdot K\), \(T = 298.15\space K\), \(V=0.755\space L\)
\(P_{CO_2}=\frac{0.0273\space mol\times62.36\space L\cdot Torr/mol\cdot K\times298.15\space K}{0.755\space L}\)
\(P_{CO_2}=\frac{0.0273\times62.36\times298.15}{0.755}\space Torr\)
\(P_{CO_2}\approx664\space Torr\)

Step3: Find the total pressure

The initial pressure of \(N_2\) is \(P_{N_2}=725\space Torr\)
By Dalton's law of partial pressures \(P_{total}=P_{N_2}+P_{CO_2}\)
\(P_{total}=725\space Torr + 664\space Torr\)

Answer:

\(1389\space Torr\)