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CHEMWORK
A steel cylinder contains 150.0 molargon gas at a temperature of 25°C and a pressure of 7.65 MPa. After some argon has been used, the pressure is 2.00 MPa at a temperature of
19°C. What mass (g) of argon remains in the cylinder?
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Answer:

Mass  = 1600 g

Explanation:

Given data:

Number of moles of argon = 150.0 mol

Initial temperature = 25°C (25+273= 298 K)

Initial pressure = 7.65 MPa

Final pressure = 2.0 MPa

Final temperature = 19°C (19+273 = 292 k)

Final number of moles = ?

Solution:

According to ideal gas law,

when volume is remain constant then the pressure of gas is directly proportional to the number of moles and temperature.

Mathematical expression,

P₁/n₁T₁   =    P₂/n₂T₂  .........(1)

P₁ = Initial pressure

n₁ = Initial number of moles

T₁ = Initial temperature  

P₂ = Final pressure

n₂ = Final number of moles

T₂ = Final temperature

Now we will put the values in equation 1.

P₁/n₁T₁   =    P₂/n₂T₂  

7.65 MPa / 150 mol×298 K = 2.0 MPa / n₂× 292K

n₂ =  2.0 MPa ×150mol×298 K/ 292K × 7.65 MPa

n₂ =  89400 mol / 2233.8

n₂ = 40.0 mol

Mass of argon remain:

Mass = number of moles × molar mass

Mass = 40.0 mol × 40.0 g/mol

Mass  = 1600 g

Initial mass:

Initial mass = number of moles × molar mass

Initial mass = 150.0 mol × 40.0 g/mol

Initial mass = 6000 g

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