Gases; Chemistry

Question

In 1783, Jacques Charles launched his first balloon filled with hydrogen gas, which he chose because it was lighter than air. The balloon, which had a volume of 31 000 L at STP, reached an altitude of 1000 m, where the pressure was 652 mmHg and the temperature was -4 ∘C.

 

What was the volume, in liters, of the balloon at these conditions?

 

Can you please explain the process of solving a question like this?

Answer 1

Standard Temperature and Pressure, (STP) is a set of conditions for experimental measurement allowing comparisons to be made between different sets of data.

 

at Standard Temperature and Pressure, 1 mole of gas takes up 22.4 L volume.

 

Use this as a conversion factor to determine the mole H₂ gas in 31,000 L at STP.

 

n/31,000 L = 1mole/22.4 L

 

n = 31,000 L * 1mole/22.4 L

 

n = 1,383.93 mole H₂

 

The mole gas does not change when the conditions (Volume, Temperature, Pressure) change.

 

Ideal Gas Equation:

 

PV =nRT

 

look up the Ideal gas constant, R in the appropriate units. (Pressure of 1 Torr is approximately equal to one millimeter of mercury, 1 mmHg)

So, I'll use R = 62.364 L Torr K⁻¹ mol⁻¹ and just convert degrees Celsius to Kelvin (273.15 - 4 = 269.15 K)

 

(652 Torr)*V = (1,383.93 mol)*(62.364 L Torr K⁻¹ mol⁻¹)(269.15 K)

 

Solve for Volume at the new conditions

 

V = 35,628.24 L