For 10 Minutes each at 27 Deg C from two identical holes nitrogen and an unknown gas are leaded in to a common vassel of 3 L Capicity. The resulting pressure is 4.18 Bar and the mixture contains 0.4 mole of nitrogen. What is the molar mass of unknowen gas.

To determine the molar mass of the unknown gas in your scenario, we can use the ideal gas law and some basic principles of stoichiometry. Let's break this down step by step.

Understanding the Problem

We have two gases being introduced into a common vessel: nitrogen (N₂) and an unknown gas. The total pressure in the vessel after both gases are released is 4.18 Bar, and we know that there are 0.4 moles of nitrogen present. The volume of the vessel is 3 liters, and the temperature is 27 degrees Celsius.

Step 1: Calculate the Total Number of Moles in the Vessel

Using the ideal gas law, which states that PV = nRT, we can rearrange it to find the total number of moles (n) in the vessel:

• P = pressure in Bar (4.18 Bar)
• V = volume in liters (3 L)
• R = ideal gas constant (0.08314 L·Bar/K·mol)
• T = temperature in Kelvin (27°C = 300 K)

Now, substituting the values into the equation:

n = PV / RT = (4.18 Bar * 3 L) / (0.08314 L·Bar/K·mol * 300 K)

Calculating this gives:

n = (12.54) / (24.994) ≈ 0.502 moles

Step 2: Determine the Moles of the Unknown Gas

Since we know there are 0.4 moles of nitrogen, we can find the moles of the unknown gas (let's call it 'x'):

x = Total moles - Moles of nitrogen = 0.502 moles - 0.4 moles = 0.102 moles

Step 3: Calculate the Molar Mass of the Unknown Gas

To find the molar mass (M) of the unknown gas, we can use the formula:

M = mass / moles

However, we need the mass of the unknown gas. We can find it using the ideal gas law again, but this time we will rearrange it to solve for mass:

mass = nRT / P

Substituting the values for the unknown gas:

mass = (0.102 moles * 0.08314 L·Bar/K·mol * 300 K) / 4.18 Bar

Calculating this gives:

mass = (2.537) / (4.18) ≈ 0.607 grams

Final Calculation of Molar Mass

Now that we have the mass of the unknown gas, we can calculate its molar mass:

M = mass / moles = 0.607 grams / 0.102 moles ≈ 5.95 g/mol

Summary

The molar mass of the unknown gas is approximately 5.95 g/mol. This value suggests that the unknown gas is likely a light gas, possibly a noble gas or a simple diatomic molecule. If you have any further questions or need clarification on any of the steps, feel free to ask!