a 1:1 mixture by weight of hydrogen and helium is enclosed in a one litre flask kept at 273k...assuming ideal behaviour partial pressure of helium was found to be 0.42 atmos....then concentration of hydrogen wud be......

To determine the concentration of hydrogen in a 1:1 mixture by weight of hydrogen and helium, we can start by analyzing the information given. We know that the partial pressure of helium is 0.42 atmospheres, and we can use this to find the concentration of hydrogen in the mixture.

Understanding the Mixture

In a 1:1 mixture by weight, we have equal masses of hydrogen (H₂) and helium (He). The molar mass of hydrogen is approximately 2 g/mol, while the molar mass of helium is about 4 g/mol. This means that for every 4 grams of helium, we have 2 grams of hydrogen.

Calculating Moles of Each Gas

Let’s assume we have 4 grams of helium. This gives us:

• Moles of helium = mass / molar mass = 4 g / 4 g/mol = 1 mol
• Since the mixture is 1:1 by weight, we have 2 grams of hydrogen, which gives us:
• Moles of hydrogen = 2 g / 2 g/mol = 1 mol

Using Dalton's Law of Partial Pressures

According to Dalton's Law, the total pressure of a gas mixture is the sum of the partial pressures of each individual gas. The partial pressure of helium is given as 0.42 atm. We can find the total pressure (P_total) using the mole fraction of helium:

The mole fraction of helium (X_He) is:

• X_He = moles of He / (moles of He + moles of H₂) = 1 / (1 + 1) = 0.5

Now, using the partial pressure of helium:

• P_He = X_He * P_total
• 0.42 atm = 0.5 * P_total

From this, we can solve for the total pressure:

• P_total = 0.42 atm / 0.5 = 0.84 atm

Finding the Partial Pressure of Hydrogen

Now that we have the total pressure, we can find the partial pressure of hydrogen (P_H₂):

• P_H₂ = P_total - P_He = 0.84 atm - 0.42 atm = 0.42 atm

Calculating Concentration of Hydrogen

To find the concentration of hydrogen, we can use the ideal gas law, which states:

• P = C * R * T

Where:

• P = partial pressure of hydrogen (0.42 atm)
• C = concentration in mol/L
• R = ideal gas constant (0.0821 L·atm/(K·mol))
• T = temperature in Kelvin (273 K)

Rearranging the equation to solve for concentration (C):

• C = P / (R * T)

Substituting the values:

• C = 0.42 atm / (0.0821 L·atm/(K·mol) * 273 K)
• C ≈ 0.0185 mol/L

Final Thoughts

The concentration of hydrogen in the mixture is approximately 0.0185 mol/L. This calculation illustrates how we can use the properties of gases and the ideal gas law to derive concentrations from partial pressures in a mixture. If you have further questions or need clarification on any part of this process, feel free to ask!