Question

A vessel of volume 100 cm3 contains 0.25 mol o2 and 0.034 mol co2 at 10.0c. Calculate the partial pressure of each component and their total pressure

Answer 1

Answer: The partial pressure of oxygen is 76.56 atm , partial pressure of carbon dioxide is 10.44 atm and the total pressure is 87 atm.

Explanation:

According to the ideal gas equation:'

$PV=nRT$

P = Pressure of the gas = ?

V= Volume of the gas = $100cm^3=0.1L$ $1L=1000cm^3$

T= Temperature of the gas = 10°C = 373 K      

R= Gas constant = 0.0821 atmL/K mol

n=  moles of gas= 0.25 +0.034 = 0.284 moles

$P=\frac{nRT}{V}=\frac{0.284\times 0.0821\times 373}{0.1}=87atm$

$x_{O_2}$ = mole fraction of oxygen=$\frac{\text {moles of }O_2}{\text {moles of }O_2+\text{moles of }CO_2}=\frac{0.25}{0.25+0.034}=0.88$,  

$x_{CO_2}$ =mole fraction of carbon dioxide=$\frac{\text {moles of }CO_2}{\text {moles of }O_2+\text{moles of }CO_2}=\frac{0.034}{0.25+0.034}=0.12$

partial pressure of oxygen = $p_{O_2}=x_{O_2}\times P=0.88\times 87=76.56atm$

partial pressure of carbon dioxide= $p_{CO_2}=x_{CO_2}\times P=0.12\times 87=10.44atmatm$

The partial pressure of oxygen is 76.56 atm , partial pressure of carbon dioxide is 10.44 atm and the total pressure is 87 atm.