Question

Question #cabd7

Answer 1

They should give the same answer of `V = 3.41 L`, assuming that the amount of gas (i.e., moles) is kept constant.

Explanation:

Using the Ideal Gas Law, `PV = nRT`.

We can take the first scenario, with

`P = 1.03 atm`
`V = 2.20 L`
`R = 0.082057338 (atm L)/(mol K)`
`T = 320.15 K`.

Which yields the following value for `n`:

`n = (PV)/(RT) = (1.03 * 2.20)/(0.082057338 * 320.15)`

`n = 0.0862559 mol`

Using that value for `n` on the latter situation, with

`P = 0.789 atm`
`T = 380.15K`.

We get the following solution for `V`:

`V = (nRT)/P = (0.0862559 * 0.082057338 * 380.15)/0.789`

`V = 3.4102357 L`

Using the 'combined gas law': `(P_1 V_1 )/ T_1 = (P_2 V_2) / T_2`.

We can just plug in the values straight away!

`V_2 = (P_1 V_1)/(T_1) * (T_2)/(P_2)`

`V_2 = (1.03 * 2.20)/(320.15) * (380.15)/(0.789)`

Which, allegedly equals,

`V_2 = 3.4102357 L`, which is as we expected.

I would say the latter method is much faster, however, it's not as 'general' as the Ideal Gas Law.