Sarah M. answered • 05/10/21
Experienced High School Science Teacher- Certified 6-12th Grades
Assuming that volume is held constant ("closed container"), your two variables in this word problem are temperature (degrees Celsius) and pressure (atm). This means you need to use the gas law equation that only has P (pressure) and T (temperature) in it, which would be Gay-Lussac's Law.
P1 / T1 = P2 / T2
Make sure that the pressure and temperature for the "before" scenario go together in one fraction, and that the pressure and temperature for the "after" scenario go together in another fraction. Note that the gas law equations only work if you convert your temperatures to Kelvin first (Celsius temp + 274.15 = Kelvin temp)
The "before" temperature is 100°C, which we must convert to Kelvin: (100 + 274.15 = 374.15Kelvin)
The "before" pressure is 2atm (no conversion needed).
These go in the first fraction:
2 atm / 374.15 Kelvin
The "after tempreature is 300°C, which we must also convert to Kelvin: (300 + 274.15 = 574.15Kelvin)
The "after" pressure is what we are solving for (we will call it "x" for now), and it will have units of atm since that is the unit of pressure we have for the "before" pressure (units must match)
These go in the second fraction:
x atm / 574.15 Kelvin
Set the two fractions equal to each other and solve using rules of Algebra I:
2 atm / 374.15 Kelvin = x atm / 574.15 Kelvin
(Multiply both sides by 574.15 Kelvin to get x by itself)
(2 atm * 574.15 Kelvin) / 374.15 Kelvin = x atm
(Plug numbers into a calculator and you have your answer)
x = 3 atm (Final Answer)
Always check for logic when you obtain a numerical answer: The temperature of the gas is increasing, so should the pressure be going up or down? Logic tells us the pressure goes up when a gas gets hotter (think of soda cans that explode when left in the trunk of your car in the summer due to the rising temperature). Therefore, it makes sense that we got a value that is greater than the 2 atm of pressure that we started with.
