Question

A 6.0-cm-diameter, 11-cm-long cylinder contains 100 mg of oxygen (O2) at a pressure less than 1 atm. The cap on one end of the cylinder is held in place only by the pressure of the air. One day when the atmospheric pressure is 100 kPa, it takes a 173 N force to pull the cap off.
A) What is the temperature of the gas?

Answer 1

Answer:

The temperature of the gas is 1197.02 K

Explanation:

From ideal gas law;

PV = nRT

Where;

P is the pressure of the gas

V is the volume of the gas

R is ideal gas constant = 8.314 L.kPa/mol.K

T is the temperature of the gas

n is the number of moles of gas

Volume of the gas in the cylindrical container = πr²h

Given;

r = 6/2 = 3 cm = 0.03 m

h = 11 cm = 0.11 m

V = π × (0.03)² × 0.11 = 3.11 × 10⁻⁴ m³ = 0.311 L

number of moles of oxygen gas = Reacting mass / molar mass

$=\frac{0.1}{32} = 0.003125, moles$

$T = \frac{PV}{nR} = \frac{100X0.311}{0.003125X8.314} =1197.02K$

Therefore, the temperature of the gas is 1197.02 K