Given that 0.28 g of dry gas occupies a volume of 354 mL at a temperature of 20°C and a pressure of 686 mmHg, how do you calculate the molecular weight of the gas?

1 Answer
May 14, 2018

Answer:

#21 g/(mol)#

Explanation:

  • We start with the Ideal Gas Law equation #PV# = #nRT#
  • Rearrange the equation to #n/V# = #P/(RT)#
  • Convert the #20^@C# to Kelvin #(K)# by adding #273#

#P# = #686 mmHg#

#R# = #(62.36367 mmHg*L)/ (mol*K)#

#T# = #293K#

  • Plug into the equation

#n/V# = #(686 mmHg)/((62.36367 mmHg*L)/ (mol*K)(293K)#

  • Multiply #62.36367# by #293# then divide by #686#

#n/V# = #0.03754 (mol)/L#

  • Convert #354mL# to #L# by dividing #354mL# by #1000#
  • Now calculate the density #d# = #M/V#

#(0.28 g) / (0.354 L)# = #0.79096 g/L#

  • Take the #g/L# and divide by #(mol)/L#

#(0.79096 g/cancelL) / (0.03754 (mol)/cancelL)# = #21 g/(mol)#