Question

A pressure cooker contains 5.68 liters of air at a temperature of 394 K. If the absolute pressure of the air in the pressure cooker is 205 pascals, how many moles of air are in the cooker? The cooker contains _______ moles of air.

Answer 1

The pressure cooker contains 0.000355 moles of air (to three significant figures).

Step-by-step explanation:

To find the number of moles of air in the pressure cooker, we can use the ideal gas law.

Ideal Gas Law

`PV=nRT`

where:

• P is the pressure measured in pascal (Pa).
• V is the volume measured in cubic meters (m³).
• T is the temperature measured in kelvin (K)
• R is the ideal gas constant (8.3144626 J·K/mol).
• n is the number of moles.

Rearrange the equation to solve for n:

`\implies n=(PV)/(RT)`

As we have been given the volume in liters, we must first convert it to cubic meters. As 1 liter = 0.001 m³ then 5.68 liters = 0.00568 m³.

Therefore, the values to substitute into the formula are:

• P = 205 Pa
• V = 0.00568 m³
• T = 394 K
• R = 8.3144626 J·K/mol

Substitute the values into the formula and solve for n:

`\implies n=(205 \cdot 0.00568)/(8.3144626 \cdot 394)`

`\implies n=0.000355444...`

`\implies n=0.000355\; \sf mol\; (3\;s.f.)`

Therefore, the pressure cooker contains 0.000355 moles of air (to three significant figures).