Question

A rigid cylinder with a movable piston contains a sample of hydrogen gas. At 330 K this sample has a pressure of 150 kPa and a volume of 3.5 L. What is the volume of this sample at STP

Answer 1

Answer:

The volume of gas at STP is 4.3 L.

Explanation:

Given data:

initial temperature of gas = 330 K

Initial pressure = 150 Kpa  (150/101.325 = 1.4804 atm)

Initial volume = 3.5 L

New pressure = 1 atm

New temperature = 273.15 K

New volume = ?

Formula

P₁V₁ / T₁   = P₂V₂ /T₂

Solution:

V₂ =  P₁V₁. T₂  / T₁ .  P₂

V₂ =  1.4804 atm. 3.5 L . 273.15 K / 330 K . 1 atm

V₂ =  1415.3 L / 330

V₂ = 4.3 L

The volume of gas at STP is 4.3 L.

Answer 2

The volume of this sample at STP is 4.3 L.

The general gas equation is given by:

PV/T = constant;

where P is pressure, V is volume and T is temperature.

Hence:

$\frac{P_1V_1}{T_1}= \frac{P_2V_2}{T_2} \\\\Given\ that:\\\\P_1=150kPa,T_1=330K,V_1=3.5L.At\ STP,P_2=100\ kPa,T_2=273.15K:\\\\\\\frac{P_1V_1}{T_1}= \frac{P_2V_2}{T_2} \\\\\frac{150*3.5}{330}=\frac{100*V_2}{273.15} \\\\V_2=4.3L$

Hence the volume of this sample at STP is 4.3 L.

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