Question

Suppose that 4 mol of gas is measured

at 4 atm pressure to have a volume of 3
L, a temperature of 270 K. If the
conditions change such that there are 3
mol at 2 atm and at 300 K, what is the
new volume?

Answer 1

Using the Combined Gas Law, the new volume of the gas is calculated to be 18 liters when the conditions change to 3 moles at 2 atm and 300 K.

Step-by-step explanation:

The problem describes a change in conditions for a sample of gas and asks for the new volume after these changes. To solve it, we can use the Ideal Gas Law in the form of Combined Gas Law since both volume and temperature, as well as the number of moles, are changing. The Combined Gas Law is stated as (P1 × V1) / (T1 × n1) = (P2 × V2) / (T2 × n2), where P is pressure, V is volume, T is temperature in Kelvins, and n is the number of moles.

Plugging in the values from the initial state, we get (4 atm × 3 L) / (270 K × 4 mol) = (2 atm × V2) / (300 K × 3 mol). Simplifying, the new volume (V2) can be calculated by cross-multiplying and solving for V2.

So the new volume is V2 = [(4 atm × 3 L × 300 K × 3 mol) / (270 K × 4 mol × 2 atm)] = (4 × 3 × 300 × 3) / (270 × 4 × 2) L = 18 L.

Therefore, under the new conditions of 3 mol at 2 atm and 300 K, the new volume of the gas is 18 liters.