A sample of gas occupies a volume of 50.0 milliliters in a cylinder with a movable piston. The pressure of the sample is 0.90 atmosphere and the temperature is 298 K. What is the volume of the sample at STP?

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Answer 1 · 2015-12-19T01:08:54

The new volume is 41 mL.

Use the combined gas law #(P_1V_1)/T_1=(P_2V_2)/T_2#.
#"STP=273.15 K and 1 atm"#

Given/Known
#P_1="0.90 atm"#
#V_1="50.0 mL"#
#T_1="298 K"#
#P_2="1 atm"#
#T_2="273.15 K"#

Unknown
#V_2#

Solution
Rearrange the equation to isolate #V_2# and solve.

#(P_1V_1)/T_1=(P_2V_2)/T_2#

#V_2=(P_1V_1T_2)/(T_1P_2)#

#V_2=(0.90cancel"atm"xx50.0"mL"xx273.15cancel"K")/(298cancel"K"xx1cancel"atm")="41 mL"#