Problem 61 - Chemistry

Question

Calculate the mass in grams of hydrogen chloride produced when \(5.6 \mathrm{~L}\) of molecular hydrogen measured at STP react with an excess of molecular chlorine gas.

Step-by-Step Solution

Answer

The mass of hydrogen chloride produced is 18.25 grams.

Step 1: Calculating the Moles of Hydrogen Gas

Calculate the number of moles of hydrogen gas using the appropriate formula: moles of H2 = volume of H2 at STP / molar volume at STP. The volume of H2 given is 5.6 L, and the molar volume at STP is 22.4 L/mol. So, moles of H2 = 5.6 L / 22.4 L/mol = 0.25 mol.

Step 2: Applying the Stoichiometry of the Reaction

The stoichiometry of the reaction is such that for every one mole of hydrogen gas, two moles of hydrogen chloride are produced. Therefore, the moles of HCl produced = 2 * moles of H2 = 2 * 0.25 mol = 0.5 mol.

Step 3: Converting Moles to Grams

Finally, we convert the moles of HCl to grams using its molar mass. The molar mass of HCl is approximately 36.5 grammes per mole. Hence, grams of HCl = moles of HCl * molar mass of HCl = 0.5 mol * 36.5 g/mol = 18.25 g.

Key Concepts

Molar Volume

The molar volume of a gas is a key concept in chemistry stoichiometry, especially when dealing with gases at standard temperature and pressure (STP). STP is defined as a temperature of 273.15 K (0 °C) and a pressure of 1 atm. Under these conditions, one mole of any ideal gas occupies a volume of exactly 22.4 liters.

This understanding helps us in converting volumes of gas to moles, which is crucial for stoichiometric calculations in chemical reactions involving gases. This is because calculations in chemistry often require us to deal with amounts in moles rather than volumes.

When you are given the volume of a gas at STP, you can determine the number of moles using the formula:

• Number of moles = Volume of gas at STP / Molar volume at STP

For example, if you have a gas measured at 22.4 L, this would correspond to exactly 1 mole of gas due to the molar volume relation.

Moles Calculation

Calculating moles is fundamental in stoichiometry, as reactions are typically balanced in terms of moles. The mole is a unit that measures the amount of substance based on the number of particles it contains, analogous to terms like a dozen or a gross.

Understanding stoichiometry involves knowing how to calculate this measure from given data. As illustrated in the exercise, converting volume to moles using the molar volume is a typical problem-solving skill. For example, if given 5.6 L of hydrogen gas at STP, you can find the number of moles by dividing by 22.4 L/mol, which gives 0.25 moles.
For chemical reactions, balanced equations guide the conversion from reactants to products in a ratio. For every mole of hydrogen gas, two moles of hydrogen chloride are formed. Hence, understanding and calculating moles according to these ratios is an integral part of solving stoichiometry problems accurately.

Molar Mass

Molar mass is another important concept in chemistry that connects the amount of a substance to its weight. The molar mass is the mass of one mole of a given substance and is usually expressed in grams per mole (g/mol).

For example, the molar mass of hydrogen chloride (HCl) is 36.5 g/mol, meaning that one mole of HCl weighs 36.5 grams. This value derives from the sum of the atomic masses of hydrogen (approximately 1 g/mol) and chlorine (approximately 35.5 g/mol).

The relevance of molar mass in stoichiometry links directly with converting moles to grams, as seen in the exercise. After calculating the moles of a substance produced or reacted, one can use its molar mass to find the respective mass in grams:

• Mass in grams = Number of moles * Molar mass

For instance, in the exercise, converting 0.5 moles of HCl to grams using the molar mass results in 18.25 grams. Understanding this conversion is critical for accurately preparing a specific amount of a chemical compound.