Question #8b6ce

1 Answer
Nov 9, 2015

Answer:

By using the Ideal Gas Law equation (#PV = nRT#)

Explanation:

Look at the given, you were given the Pressure (P), Temperature (T), Volume (V) and mass (m) of an unknown gas.

P = 79.97 kPa
V = 4.167 L
T = #30^@C#
m= 20.83 g

Based on the given, you can definitely use the Ideal Gas Law equation to find the molar mass of the gas, where R is a constant equal to #0.0821 (L*atm)/(mol*K)#.

But first, we need to convert units:
P = #79.97 cancel "kPa"# x #(0.00986923 atm)/(1 cancel "kPa")# = #0.789 atm#
V = #4.167 L#
T = #30^@C# + #273.15 K# = #303.15 K#
m= #"20.83 g"#

Now we are ready to compute.

#PV = nRT#

#(0.789 atm) (4.167 L)# = #n# (#0.0821 (L*atm)/(mol* cancel K)#) (#303.15 cancel K#)

#"3.288 atm"*L# = #n# (#24.8583 (L*atm)/(mol)#)

n = #(3.288 cancel "atm"* cancel L)/(24.8583 cancel L* cancel (atm)/"mol")# = 0.1322 mol

Since molar mass is defined as weight of substance over the number of moles substance or

MM = #("g substance")/("mol substance")#

then

MM = #("20.83 g")/("0.1322 mol")#

MM = #color (red) (157.56 g/"mol")#

Therefore, the molar mass of the unknown gas is 157.56 g/mol.