A cylinder 1.00m tall with inside diameter 0.120 m is used to hold propane gas(molar mass 44.1 g/mol) for use in a barbecue. It is initially filled in with gas until the gauge pressure is 1.30 x 10^6 Pa and the temperature is 22 degree Celsius. The temperature of the gas remains constant as it is partially emptied out of the tank, until the gauge pressure is 2.50 x 10^5 Pa. Calculate the mass of propane that has been used?

The mass of propane gas which has been used in a barbecue is 195.05 g

Explanation:

Given

We are given a tank with length L =1 in and radius r = 0.06 m filled with a propane gas with pressure p = 1.3 x 10^6 Pa at temperature T = 22 C° = 295K and the volume V employed by  

V=πr^2L

  =π(0.06m)^2*1m

  =0.0113m^3

Some of this gasemptied to be used and the pressure decreased to 2.50 x 10^5 Pa and definitely mass also reduced and we were asked to calculate the mass of gas that has been used.  

Solution

In this case, we have two states: 1st state is propane gas has mass mi and pressure pi = 1.3 x 10^6 Pa  

2nd state is propane gas has mass m2 remains in the tank after a part of the gas is emptied and pressure p2 = 2.50 x 10^5 Pa

We are given p1 and p2 and must calculate mi first to find m2 which will lead us to find the amount of the gas that has been used. So in first state we would apply Ideal gas law to find the initial mass m1

 p1*V=nRT             (1)

Where n is the number of moles and could sub with its value with m/M where Al is the molar mass of propane gas and equals 44.1 gimol as given.  to find the relation between the number of moles, the mass and the molar mass) . So equation (1) would be  

 p1*V=(m1/M)*RT     (2)

By sub with all given values in equation (2) and solve for mi  

m1 =  p1*V*M/RT

    =264.13 g

By back to equation (2) we would find that the relation between pressure and mass is proportional (Note that the volume, the temperature, R and molar mass are constant). So we would extract a relation between p and m for the two states by  

p1/p2=m1/m2

By sub with all values of p1, p2 and m1 and solve for m2

m2=m1*p2/p1

    =69.08 g

Now we found the mass of remaining gas in the tank after a part of gas was used. lb calculate the mass of propane gas that has been used it would be given by  

m1-m2 = 264.13 g - 69.08 g  

           =195.059 g

The mass of propane gas which has been used in a barbecue is 195.05 g

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