) The volume of a balloon was 50,200 litres. If the temperature at ground level was 25 degree celcius and the atmospheric pressure was
720mm Hg. How many moles of Hydrogen gas were needed to
fill the balloon?

1943.1 moles

Explanation:

From the question given above, the following data were obtained:

Volume (V) = 50200 L

Temperature (T) = 25 °C

Pressure (P) = 720 mmHg

Number of mole (n) of H₂ =?

Next, we shall convert 25 °C to Kelvin temperature. This can be obtained as follow:

T(K) = T(°C) + 273

Temperature (T) = 25 °C

Temperature (T) = 25 °C + 273

Temperature (T) = 298 K

Next, we shall convert 720 mmHg to atm. This can be obtained as follow:

760 mmHg = 1 atm

Therefore,

720 mmHg = 720 mmHg × 1 atm / 760 mmHg

720 mmHg = 0.947 atm

Thus, 720 mmHg is equivalent to 0.947 atm

Finally, we shall determine number of mole of Hydrogen gas, H₂, needed to fill the balloon as follow:

Volume (V) = 50200 L

Temperature (T) = 298 K

Pressure (P) = 0.947 atm

Gas constant (R) = 0.0821 atm.L/Kmol

Number of mole (n) of H₂ =?

PV = nRT

0.947 × 50200 = n × 0.0821 × 298

47539.4 = n × 24.4658

Divide both side by 24.4658

n = 47539.4 / 24.4658

n = 1943.1 moles

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