In 1783, Jacques Charles launched his first balloon filled with hydrogen gas, which he chose because it was lighter than air. If the balloon had a volume of 31 000 L, how many kilograms of hydrogen were needed to fill the balloon at STP?
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Verified step by step guidance

1. Step 1: Recall the conditions of STP (Standard Temperature and Pressure). At STP, the temperature is 273.15 K, the pressure is 1 atm, and 1 mole of any ideal gas occupies 22.4 L.
2. Step 2: Use the volume of the balloon (31,000 L) and the molar volume of a gas at STP (22.4 L/mol) to calculate the number of moles of hydrogen gas. The formula is: \( \text{moles of H}_2 = \frac{\text{volume of H}_2}{\text{molar volume at STP}} \).
3. Step 3: Determine the molar mass of hydrogen gas (H₂). Since each hydrogen atom has a molar mass of approximately 1.008 g/mol, the molar mass of H₂ is \( 2 \times 1.008 = 2.016 \ \text{g/mol} \).
4. Step 4: Convert the moles of hydrogen gas to grams using the formula: \( \text{mass of H}_2 = \text{moles of H}_2 \times \text{molar mass of H}_2 \).
5. Step 5: Convert the mass of hydrogen gas from grams to kilograms by dividing by 1,000. The formula is: \( \text{mass in kg} = \frac{\text{mass in g}}{1000} \).

Key Concepts

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in chemistry that relates the pressure, volume, temperature, and number of moles of a gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin. This law allows us to calculate the amount of gas needed under specific conditions, such as Standard Temperature and Pressure (STP).

Standard Temperature and Pressure (STP)

Standard Temperature and Pressure (STP) is a reference point used in chemistry to define the conditions under which gas measurements are made. STP is defined as a temperature of 0 degrees Celsius (273.15 K) and a pressure of 1 atmosphere (101.3 kPa). At STP, one mole of an ideal gas occupies a volume of 22.4 liters, which is crucial for calculating the amount of gas required to fill a given volume.

Molar Mass of Hydrogen

The molar mass of hydrogen is the mass of one mole of hydrogen gas (H2), which is approximately 2 grams per mole. This value is essential for converting between the volume of hydrogen gas and its mass when using the Ideal Gas Law. Knowing the molar mass allows us to determine how many kilograms of hydrogen are needed to fill the balloon at STP based on the volume provided.