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
