Question

The gases in a hair spray can are at a temperature of 27OC and a pressure of 30 lbs/in2. If the gases in the can reach a pressure of 90 lbs/in2, the can will explode. To what temperature in kelvin must the gases be raised in order for the can to explode? Assume constant volume. (1 sig fig for answer)

50 points

Answer 1

In order to solve this problem, you can use the Ideal Gas Law, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in kelvin.
As we know that the volume is constant, we can say that PV1 = PV2.
P1V1 = P2V2

We also know that P1 = 30 lbs/in2, P2 = 90 lbs/in2

Rearranging the equation, we can find the temperature T2:
T2 = (P1V1/nR) * (P2/P1) = (30 lbs/in2 * V1/nR) * (90 lbs/in2/30 lbs/in2)

P1 and V1 are known. We need to find T2.
T2 = (27+273.15) * (90/30) = (300) * 3 = 900 K

So, the temperature in kelvin must be raised to 900 K in order for the can to explode.