Question

A 10 liter flask at 298 K contains a gaseous mixture of O2 and CO2 at 1 atmosphere. Which statement is true for the partial pressures of O2 and CO2 if 0.2 mole of O2 is present in the flask? (Given the universal gas constant R = 0.082 L∙atm/K∙mol)

Answer 1

Answer:

The partial pressures of O₂ and CO₂ are 0.489 atm and 0.511 atm respectively.

Explanation:

From the Questions we are given;

Volume = 10 Liter

Temperature = 298 K

Pressure = 1 atm

We need to calculate the partial pressures of O₂ and CO₂

Step 1 : Number of moles of gaseous mixture

Using the ideal gas equation;

PV =nRT, where P is the pressure, V is the volume, n is the number of moles, T is the temperature in K and R is the ideal gas constant (0.082 L∙atm/K∙mol)

Therefore;

$n =\frac{PV}{RT}$

$n = \frac{(10)(1)}{(298)(0.082)}$

Solving for n

$n = 0.409 moles$

Step 2: Moles of CO₂

Total number of moles of the mixture = 0.409 moles

Moles of Oxygen = 0.2 moles

Therefore;

Moles of CO₂ = 0.409 moles - 0.2 moles

                      = 0.209 moles

Step 3: Partial pressures of O₂ and CO₂

$Partial pressure = \frac{No. of moles}{Total number of moles}(total pressure)$

Therefore;

Partial pressure of Oxygen gas

$= \frac{number of moles of Oxygen}{Total number of moles} (Total pressure)$

$= \frac{0.2}{0.409}(1)\\= 0.489 atm$

Partial pressure of CO₂

$= \frac{number of moles of CO₂}{Total number of moles} (Total pressure)$

$= \frac{0.209}{0.409}(1)\\= 0.511 atm$

Thus, the partial pressures of O₂ and CO₂ are 0.489 atm and 0.511 atm respectively.