At 7.0ºC, the volume of a gas is 49 mL. At the same pressure, its volume is 74 mL at what temperature?

Answer 1

As an addition to the answer provided by @Anthony T, I submit the following:

When the pressure is constant, we can us Charles' Law which is V1/T1 = V2/T2

V1 = initial volume = 49 ml

T1 = initial temperature in Kelvin = 7.0º + 273 = 280K

V2 = final volume = 74 ml

T2 = final temperature in Kelvin = ?

Solving for T2 we have...

49 ml / 280K = 74 ml / T2

T2 = 423K

T2 = 423 -273 = 150ºC

Answer 2

You can use the ideal gas equation to solve this one.

In the initial case, PV1 = nRT1 where V1 is the initial volume but expressed in liters, 0.049 L and T1 is the initial temperature expressed in degrees K, 280 °K.

 In the final case, the temperature is T2 and the volume is T2 = 0.074 L.

Now let’s express the ideal gas equation initially as P = nRT1/ V1 and the equation for the second state as P = nRT2/V2.

Since the pressure P doesn’t change, we can equate the two equations to get

nRT1/V1 = nRT2/V2. The n, and R cancel out leaving T1/V1 = T2/V2.

V1, V2 and T1 are given, so solve this last equation for T2.

T2 = 280 K / 0.049 L x 0.074 L = 422.9 K. (We could have used the volume left as mL

and got the same answer).