Question

A welder using a tank of volume 7.60×10−2 m3 fills it with oxygen (with a molar mass of 32.0 g/mol ) at a gauge pressure of 3.05×105 Pa and temperature of 35.4 ∘C. The tank has a small leak, and in time some of the oxygen leaks out. On a day when the temperature is 20.8 ∘C, the gauge pressure of the oxygen in the tank is 1.95×105 Pa.Find the initial mass of oxygen. (in Kg)

Answer 1

The initial mass of oxygen is 0.38538 Kg.

Step-by-step explanation:

Given that,

Volume of tank
`V= 7.60*10^(-2)\ m^3`

Molar mass = 32.0 g/mol

Gauge pressure
`P_(g)=3.05*10^(5)\ pa`

Initial temperature = 35.4°C

Final temperature = 20.8°C

Gauge pressure
`P_(g)=1.95*10^(5)\ Pa`

We need to calculate initial pressure

Using formula of pressure

`P_(1)=P_(atm)+P_(g)`

Put the value into the formula

`P_(1)=1.013*10^(5)+3.05*10^(5)`

`P_(1)=4.063*10^(5)\ Pa`

We need to calculate the number of moles

Using equation of ideal gas

`PV= nRT`

`n_(i)=(P_(1)V_(1))/(RT_(1))`

Put the value into the formula

`n_(i)=(4.063*10^(5)*7.60*10^(-2))/(8.314*(273+35.4))`

`n_(i)=12.043\ moles`

We need to calculate the initial mass of oxygen

Using formula of mass

`M=m_(m)n_(i)`

Put the value into the formula

`M=32.0*12.043`

`M=385.38\ g`

`M=0.38538\ kg`

Hence, The initial mass of oxygen is 0.38538 Kg.