Question

Hydrogen holds promise as an environment-friendly fuel. How many grams of H₂ gas are present in a 54.0 L fuel tank at a pressure of 2501 lb/in² (psi) at 20.0°C? Assume that 1 atm = 14.7 psi.

Answer 1

Step 1: Explanation

The ideal gas law is the equation of state of a hypothetical ideal gas. It is a good approximation of the behavior of many gases under many conditions.

We know the ideal gas equation, PV = nRT

where, R=universal gas constant ( it may vary in unit like 0.08206 L-atm mol-1 K-1 , 62.36 torr-L mol-1 K-1 )

T=Temperature ( Unit = Kelvin )

P=Pressure ( Unit= atm )

V=Volume ( Unit=Litre )

n=moles ( Unit = mol )

Step 2: Calculation of moles

Temperature(T) = 20 °C = ( 20+273.15) K = 293.15 K

Pressure (P) = 2501 psi = 170.136 atm

[ because 1 atm = 14.7 psi so, 2501 psi = ( 2501 psi × ( 1 atm / 14.7 psi) = 170.136 atm ]

Volume(V) = 54 L

on substituting the value

=> PV = nRT

=> moles(n) = PV / RT = ( 170.136 atm × 54 L) / ( 0.08206 L-atm /mol-K  × 293.15 K ) = 381.92 mol

Step 3: Calculation of mass

Molar mass of H2 = 2.01588 g/mol

Mass of H2 = molar mass × moles = 2.01588 g/ mole × 381.92 mole = 770 g