Can anyone please help me with my homework? I am stuck! Many thnaks in advance!

Question

Can anyone please help me with my homework? I am stuck! Many thnaks in advance!

1. A mixture of methane and hydrogen gases contains methane at a partial pressure of  377 mm Hg and hydrogen at a partial pressure of 467 mm Hg. What is the mole fraction of each gas in the mixture

2. What volume of oxygen gas is required to react completely with 0.292 mol of propane (C3H8) according to the following reaction at 0°C and 1 atm?

3. What volume of hydrogen gas is produced when 0.744 mol of sodium reacts completely according to the following reaction at 0°C and 1 atm?

Explanation / Answer

1.

PCH4 = XCH4 * Ptotal

PH2 = XH2 * Ptotal

So,

PCH4 / PH2 = XCH4 / XH2

So,

XCH4 / XH2 = 377 / 467

XCH4 / XH2 = 0.807

XCH4 = 0.807 * XH2

We know,

Sum of mole fraction of all components = 1

XCH4 + XH2 = 1

0.807 * XH2 + XH2 = 1

XH2 = 1 / 1.807 = 0.553

So ,

XH2 = 0.553   and XCH4 = 1 - 0.553 = 0.446

2.

Balanced reaction is

C3H8 + 5O2 ---------> 3CO2 + 4H2O

1 mol of C3H8 reacts with 5 mol of O2

0.292 mol of C3H8 reacts with 5 * 0.292 = 1.46 mol of O2

Now,

moles = given volume / molar volume at STP

1.46 mol = V / 22.414 L

V = 32.72 L

So, Volume of O2 gas required = 32.72 L

3.

Na + H2 ------> 2 NaH

1 mol of Na reacts with 1 mol of H2

0.744 mol of Na reacts with 0.744 mol of H2

Again,

moles = given volume / molar volume

0.744 mol = V / 22.414 L

V = 16.676 L

So,

Volume of H2 required = 16.676 L

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