Question

A 6.0 L sample at 25°C and 2.00 atm contains 0.5 mole of a gas. If an additional 0.25 mole of gas at the same pressure and temperature are added, what is the final total volume of the gas?

Answer 1

Using the Ideal Gas Law and the direct relationship between moles and volume, the final total volume after adding 0.25 mole of gas to the original 0.5 mole of gas at constant pressure and temperature is 9.0 L.

Step-by-step explanation:

To determine the final total volume of gas after adding 0.25 mole to the existing 0.5 mole of gas at the same pressure and temperature, we can use the Ideal Gas Law, which states that PV = nRT. Assuming the temperature (T) and the pressure (P) remain constant, the relationship between number of moles (n) and volume (V) is directly proportional. Initially, we have 0.5 mol of gas occupying 6.0 L. After adding 0.25 mol, so the total becomes 0.75 mol. Since the pressure and temperature remain constant, we can use the ratio V1/n1 = V2/n2, which simplifies to V2 = (n2/n1) × V1. Plugging in the numbers, the final volume (V2) can be calculated as follows:

• n1 = 0.5 mol
• V1 = 6.0 L
• n2 = 0.75 mol
• V2 = (0.75 mol / 0.5 mol) × 6.0 L = 9.0 L

Therefore, the final total volume of the gas after adding an additional 0.25 mole of gas is 9.0 L.