A balloon that can hold 85 L of air is inflated with 7.056 grams of H2 gas at a pressure of 101.3 kPa. What is the temperature, in Celsius, of the balloon.

Temperature is 258.32°C

Using the ideal gas equation;

PV = nRT        (i)

Where;

P = Pressure of the gas

V = Volume of the gas

n = number of moles of the gas

R = Gas constant = 8.31 J/mol · K

T = Temperature

Given:

mass of H₂ gas = 7.056 grams

Volume of the gas = 85L = 8.5 x 10⁻³m³

Pressure of the gas = 101.3kPa = 101.3 x 10³Pa = 1.013 x 10⁵Pa

Steps:

(i) Using the mass of the gas, calculate the number of moles using the relation:

n = m / M         (ii)

Where;

m = mass of H₂ = 7.056g

M = Molar mass of H₂ = 1g/mol

Substitute these values into equation (ii) as follows:

n = 7.056g / (1g/mol)

n = 7.056mol

(ii) Now calculate the temperature of the balloon by substituting the necessary values into equation (i)

(1.013 x 10⁵Pa)(8.5 x 10⁻³m³) = (7.056mol) (8.31 J/mol · K)(T)

T = (1.013 x 10⁵Pa)(8.5 x 10⁻³m³) ÷ (7.056mol) (8.31 J/mol · K)

Solving the above gives

T = 14.68K

Convert this to Celsius

T = 273 - 14.68

T = 258.32°C

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