Question

A steel cylinder of oxygen is being store in a room at 25.0 °C under a pressure of 1250 atm. What pressure would be exerted by the gas if the container were transported across the desert at 40.0°C?

a. 1750 atm

b. 15700 atm

c. 1980 atm

d.1310 atm

Answer 1

P₂ = 1312.9 atm

Step-by-step explanation:

Given data:

Initial temperature = 25°C

Initial pressure = 1250 atm

Final temperature = 40°C

Final pressure = ?

Solution:

Initial temperature = 25°C (25+273.15= 298.15 K)

Final temperature = 40°C (40+273.15 = 313.15 k)

According to Gay-Lussac Law,

The pressure of given amount of a gas is directly proportional to its temperature at constant volume and number of moles.

Mathematical relationship:

P₁/T₁ = P₂/T₂

Now we will put the values in formula:

1250 atm /298.15 K = P₂/ 313.15 k

P₂ = 1250 atm × 313.15 k / 298.15 K

P₂ = 391437.5 atm. K /298.15 K

P₂ = 1312.9 atm