Gases...Finding mass escape

1. The problem statement, all variables and given/known data



A cylinder containing 19 kg of compressed air at a pressure 9.5 times that of the atmosphere is kept in a store at 7 degrees Celsius. When it is moved to a workshop where the temperature is 27 degrees Celsius a safety valve on the cylinder operates, releasing some of the air. If the valve allows air to escape when its pressure exceeds 10 times that of the atmosphere, Calculate the mass of air that escapes..



2. Relevant equations



PV= nRT



where P - Pressure

V- Volume

n- number of moles

R- universal gas constant (8.314 J / mol. K )

T - temperature on Kelvin



Moles = mass / Mr



pressure1 9.5 x 760 mmHg = 7220 mmHg



Temperature1 7°C = 280 K



pressure2 10 x 760 mmHg = 7660 mmHg



Temperature 27°C = 300 K



3. The attempt at a solution



I assumed that the volume was constant and at STP 22.4 x 10^-3 m³



rearranging the equation PV = nRT, placing n as the subject



With Pressure 1 and Temperature 1



n = 7220(22.4 x 10^-3) / 8.314(280)



n = 0.0694 moles



With Pressure 2 and Temperature 2



n = 7660(22.4 x 10^-3) / 8.314(300)



n = 0.0687 moles



Rearranging the equation for moles to find Mr, using the initial mass and moles from pressure 1 and temperature 1



Mr = 19 kg / 0.0694 moles



Mr = 274



using the Mr value calculated to find mass from pressure 2 and temperature 2



274 x 0.0687 = 18.82 kg



subtracting the above value from the initial mass 19



19 - 18.82= 0.18 kg





Im not sure if i worked this out right...or if it makes any sense at all but it was as close i could of gotten in attempting this problem... please any assistance of guidance will be grateful....

1. The problem statement, all variables and given/known data







2. Relevant equations







3. The attempt at a solution