Question

A tank contains 135 moles of neon gas. It has a pressure of 47 atm at a temperature of 65 C. Calculate the

volume of the tank.

Show your work

Answer 1

79.7 L = 0.0797 m³

Step-by-step explanation:

Use the Ideal Gas Law to calculate the volume of the tank containing 135 moles of neon gas, that has a pressure of 47 atm at 65°C.

Ideal Gas Law

`\boxed{PV=nRT}`

where:

• P is the pressure measured in atmosphere (atm).
• V is the volume measured in liters (L).
• n is the number of moles.
• R is the ideal gas constant (0.082057366080960 atm L mol⁻¹ K⁻¹).
• T is the temperature measured in kelvin (K).

First convert the temperature from Celsius to kelvin by adding 273.15:

`\implies T=65+273.15=338.15\; \sf K`

Therefore, the values to substitute into the equation are:

• P = 47 atm
• n = 135 mol
• R = 0.082057366080960 atm L mol⁻¹ K⁻¹
• T = 338.15 K

As we want to find the volume, rearrange the equation to isolate V:

`V=(nRT)/(P)`

Substitute the values into the equation and solve for V:

`\implies V=(135 \cdot 0.0820573 \cdot 338.15)/(47)`

`\implies V=(3645.93927...)/(47)`

`\implies V=79.7008356...`

`\implies V=79.7\; \sf L\;(3\;s.f.)`

Therefore, the volume of the tank is 79.7 liters (rounded to three significant figures).

If the answer should be in m³, simply divide the number of liters by 1000 since 1 L = 1000 m³. Therefore, the volume is 0.0797 cubic meters (3 s.f.).