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

Answer:

The initial mass of oxygen is 0.38538 Kg.

Explanation:

Given that,

Volume of tank $V= 7.60\times10^{-2}\ m^3$

Molar mass = 32.0 g/mol

Gauge pressure $P_{g}=3.05\times10^{5}\ pa$

Initial temperature = 35.4°C

Final temperature = 20.8°C

Gauge pressure $P_{g}=1.95\times10^{5}\ Pa$

We need to calculate initial pressure

Using formula of pressure

$P_{1}=P_{atm}+P_{g}$

Put the value into the formula

$P_{1}=1.013\times10^{5}+3.05\times10^{5}$

$P_{1}=4.063\times10^{5}\ Pa$

We need to calculate the number of moles

Using equation of ideal gas

$PV= nRT$

$n_{i}=\dfrac{P_{1}V_{1}}{RT_{1}}$

Put the value into the formula

$n_{i}=\dfrac{4.063\times10^{5}\times7.60\times10^{-2}}{8.314\times(273+35.4)}$

$n_{i}=12.043\ moles$

We need to calculate the initial mass of oxygen

Using formula of mass

$M=m_{m}n_{i}$

Put the value into the formula

$M=32.0\times12.043$

$M=385.38\ g$

$M=0.38538\ kg$

Hence, The initial mass of oxygen is 0.38538 Kg.