Question

A 0.0625 tank contains 0.0925kg nitrogen at a gauge pressure of 5.17atm.Find the temperature of the gas in degree Celsius​

Answer 1

-271.96 °C

Step-by-step explanation:

We are given;

• Volume of the tank as 0.0625 L
• Mass of nitrogen gas as 0.0925 kg or 92.5 g
• Pressure of the gas as 5.17 atm

we are required to calculate the temperature of the gas.

Step 1: Calculate the number of moles of nitrogen gas

Moles = Mass ÷ Molar mass

Molar mass of nitrogen gas = 28.0 g/mol

Therefore;

Moles of N₂ = 92.5 g ÷ 28.0 g/mol

= 3.304 moles

Step 2: Calculate the temperature of the gas;

According to the ideal gas equation;

PV = nRT , where n is the number of moles and R is the ideal gas constant, 0.082057 L.atm/mol.K

Rearranging the formula;

T = PV ÷ nR

= ( 5.17 atm × 0.0625 L) ÷ (3.304 moles × 0.082057)

= 1.19 K

But, °C = K - 273.15

Therefore;

T = 1.19 K - 273.15

= -271.96 °C

Thus, the temperature of the gas will be -271.96 °C