Question #120316

Hydrogen gas is generated by the decomposition of water to fill a 1.1 kL weather balloon at 20°C and 100.0 kPa. What is the mass of hydrogen required?

Expert's answer

P = 100.0 kPa

V = 1.1 kL = 1100 L

T = 20°C = 293 K

R = 8.314 kPa L mo^{-1} K^{-1}

**Solution:**

The decomposition reaction of water:

2H_{2}O → 2H_{2} + O_{2}

Ideal Gas Law can be used.

Ideal Gas Law can be expressed as: PV=nRT

To find the moles of H_{2}, solve the equation for n:

n = PV/RT

Moles of H_{2} = n(H_{2}) = (100.0 kPa × 1100 L) / (8.314 kPa L mol^{-1} K^{-1} × 293 K) = 45.156 mol

Moles of H_{2} = Mass of H_{2} / Molar mass of H_{2}

The molar mass of H_{2} is 2.016 g/mol.

Finally, the mass of H_{2} is:

m(H_{2}) = n(H_{2}) × M(H_{2}) = (45.156 mol) × (2.016 g/mol) = 91.034 g = 91 g

The mass of H_{2} is 91.0 g

**Answer: 91 g is the mass of hydrogen required.**

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