Question #26795

2 Answers
Apr 16, 2017

Answer:

#T_2=2770"°C"#

Explanation:

Gay-Lussac's Law states that for a constant volume and pressure of gas, #P_1/T_1=P_2/T_2#. Rearranged to solve for #T_2#, this is #T_2=(T_1 times P_2)/P_1#.

Keeping in mind that temperature has to be in Kelvin, #T_1=31"°C"+273=304"K"#

Plugging in the values from the problem,
#T_2=(304"K" times 7450"Torr")/(745"Torr")=3040"K"#

And to convert back to Celsius to answer the question,
#T_2=3040"K"-273=2767"°C"#, and rounding to the appropriate number of significant figures gives #2770"°C"#.

Apr 16, 2017

Answer:

The Celsius temperature required to reach #"7450 torr"# is #"2770"^@"C"#.

Explanation:

This is an example of Gay-Lussac's law , which states that the pressure of a gas is directly proportional to its temperature in Kelvins , as long as the amount and volume is held constant. This means that as the pressure increases, the temperature increases, and vice-versa. The equation to use is:

#P_1/T_1=P_2/T_2#

Given:
#P_="745 torr"#
#T_1="31"^@"C"+273.15="304 K"#
#P_2="7450 torr"#

Unknown: #T_2#

Solution
Rearrange the equation to isolate #T_2#. Substitute the given values into the equation and solve.

#T_2=(P_2T_1)/P_1#

#T_2=(7450color(red)cancel(color(black)("torr"))xx304"K")/(745color(red)cancel(color(black)("torr")))="3040 K"# (rounded to three significant figures)

Convert Kelvin Temperature to Celsius Temperature

To convert the temperature in Kelvins to degrees Celsius, subtract #273.15# from the Kelvin temperature.

#3040"K"-273.15=2770^@"C"#, rounded to three significant figures.