The temperature of 200.0 mL of a gas originally at STP is changed to -25C at constant volume. Calculate the pressure of the gas in atm? (0.91 atm)

gay-lussac's law

1 Answer
Dr. K.
Aug 1, 2018

0.91 atm

Explanation:

At standard temperature and pressure ( STP ), the system has a temperature of 0 Celsius and pressure which is equal to the atmosphere, 1 atm.

#T_1 = "0 Celsius"#
#P_1="1 atm"#

A change in temperature causes a change in the pressure:
#T_2 = "-25 Celsius"#
#P_2 = ?#

The volume of the gas remains constant at 200.0 mL, while its pressure and temperature changed. We will be able to calculate the pressure, #P_2#, after the temperature change using the Gay-Lusaac's law:

#(P_1)/(T_1)=(P_2)/(T_2)#

Before plugging in the values to the formula, we need to first convert the temperatures from Celsius to Kelvin:

#T_1 = "0 Celsius" + 273.15 = 273.15 K#

#T_2 = "-25 Celsius" + 273.15 = 248.15 K #

Plugging in the values to find #P_2#:

#("1 atm")/("273.15 K")=(P_2)/("248.15 K")#

#P_2 = ("1 atm")/("273.15 K") xx "248.15 K" = "0.91 atm"#

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