Answer:
5.1% increase
Step-by-step explanation:
We can use the combined gas law to understand how to answer this question. It states:
P1V1/T1 = P2V2/T2,
where P, V, and T are pressure, volume, and temperature, for the initial (1) and final(2) conditions.
It is very important to note that all gas law calculations require the temperature to be in Kelvin. It is immaediately obvious why that is: Since temperature in in the denominator, a Celsius reading of 0 degrees would result in division by zero, which is undefined.
We want to find the change in pressure when temperature is changed. We aren't given starting or final pressures. This is OK since we are asked for a relative increase. We are also not told the volume, so we must assume it does not change. Assign 1 liter for the violume for convenience. So let's assume P1 = 1 atm for convenience and enter the data. We are also not told the volume, so we miust assume it does not change. Assign 1 liter for the violume for convenience. Add 273.15 to C to find K.
Lets rearrange the equation to find the ratio of P2/P2:
P1V1/T1 = P2V2/T2
V1/T1 = (P2V2/T2)/P1
V1/T1 = (V2/T2)(P2/P1)
(V1/T1)*(T2/V2)= (V2/T2)(P2/P1)
(V1/T1)*(T2/V2)= (V2/T2)(P2/P1)
P2/P1 = (V1/V2)*(T2/T1)
Note how we've grouped the variables: both the volume and temperature are ratios. This helps us understand what to expect from the change in conditions. Volunes remain the same, so (V1/V2) reduces to 1 and the untis cancel. Volume has no impact on the pressure, which makes sense because it does not change. The ratio of temperatures (T2/T1, in Kelvin) tells us that the P2/P2 ratio will go up as the temperature rises. That makes sense. Since we are using Kelvin, the ratio is (288.15/287.15) or slightly more than 1. This also makes sense. Pressure will go up if the gas warms up.
Make a table for the data and then enter it:
P1 = 1 atm
V1 and V2 = 1 L
T1 = 287.15
T2 = 288.15
P1V1/T1 = P2V2/T2
V1/T1 = (P2/P1)V2/T2
(P2V1) = (V1/T1)*(T2/V2)
(P2V1) = (V1/V2)*(T2/T1)
(P2/P1) = (1L/1L)*(288.15K/287.15K)
(P2/P1) = 1.051
(1.051 - 1.00) = 0.051 atm
(0.051 atm/1.00 atm) = 0.051
The resulting pressure is 5.1% higher