Problem 95 - Chemistry Matter and Change

Question

Oxygen Consumption If 5.00 L of hydrogen gas, measured at a temperature of \(20.0^{\circ} \mathrm{C}\) and a pressure of 80.1 \(\mathrm{kPa}\) , is burned in excess oxygen to form water, what mass of oxygen will be consumed? Assume temperature and pressure remain constant.

Step-by-Step Solution

Answer

2.64 grams of oxygen will be consumed.

Step 1: Write the balanced chemical equation

Start by writing the balanced chemical equation for the burning of hydrogen gas in oxygen to form water. The reaction is \( 2H_2(g) + O_2(g) \rightarrow 2H_2O(l) \). This equation shows that two moles of hydrogen gas react with one mole of oxygen gas to produce water.

Step 2: Calculate the moles of hydrogen gas

Use the ideal gas law, \( PV = nRT \), to find the number of moles of hydrogen gas. Given: \( P = 80.1 \text{ kPa} \), \( V = 5.00 \text{ L} \), \( T = 20.0\text{ C} + 273.15 \text{ to convert to Kelvin} \), \( R = 8.314 \text{ J/(mol K)} \). Convert pressure to pascals (1 kPa = 1000 Pa). Calculate: \( n = \frac{PV}{RT} = \frac{(80.1\times1000)\times5.00}{8.314\times293.15} \approx 0.165 \text{ moles}\).

Step 3: Determine the moles of oxygen gas needed

Using stoichiometry from the balanced equation, for every 2 moles of hydrogen, 1 mole of oxygen is needed. So, \( 0.165 \text{ moles of } H_2 \) needs \( \frac{0.165}{2} = 0.0825 \text{ moles of } O_2 \).

Step 4: Calculate the mass of oxygen consumed

Find the mass of \( 0.0825 \text{ moles of } O_2 \) using the molar mass of oxygen (\( O_2 = 32.00 \text{ g/mol} \)). Calculate: \( \text{mass} = 0.0825 \times 32.00 = 2.64 \text{ grams of } O_2 \).

Key Concepts

Chemical Reaction

A chemical reaction involves the transformation of one or more substances into different substances, known as products. In the case of hydrogen burning, hydrogen gas (\(H_2\)) reacts with oxygen gas (\(O_2\)) to form water (\(H_2O\)). This is a classic example of a combustion reaction. Such reactions usually involve a reactant burning in the presence of oxygen and are significant for understanding energy conservation and transformation.Key points to remember about chemical reactions:

• Reactants are the starting materials in a chemical reaction.
• Products are the substances created from the reaction.
• The reaction we consider is exothermic, meaning it releases energy (heat).

Understanding the nature of the reactants and products is crucial for predicting the outcome and energy changes of a reaction.

Ideal Gas Law

The Ideal Gas Law is a fundamental equation that relates the pressure, volume, temperature, and number of moles of a gas. It is expressed as \( PV = nRT \), where:

• \( P \) = pressure of the gas
• \( V \) = volume of the gas
• \( n \) = number of moles of the gas
• \( R \) = ideal gas constant (\( 8.314 \ \text{ J/(mol K)} \))
• \( T \) = temperature in Kelvin

In the given exercise, the Ideal Gas Law helps determine the number of moles of hydrogen gas. Since temperature and pressure are constants, this law simplifies calculations and predictions related to gaseous reactants and products.To convert Celsius to Kelvin, add 273.15 to the Celsius temperature. Always remember to maintain consistent units when performing these calculations.

Molar Mass

Molar mass is the mass of one mole of a substance, expressed in grams per mole (\( \text{g/mol} \)). It serves as a bridge between the amount of substance in moles and the mass in grams. For instance, the molar mass of oxygen (\(O_2\)) is 32.00 \(\text{g/mol}\) due to its composition of two oxygen atoms, each having an atomic mass of approximately 16.00 \(\text{g/mol}\).Understanding molar mass is crucial when calculating the mass of reactants or products in a chemical equation. In the problem, we need to find the mass of oxygen consumed. Knowing the moles of oxygen and its molar mass allows us to determine the total mass used in the reaction, which is a vital aspect of stoichiometry.

Balanced Chemical Equation

A balanced chemical equation represents a chemical reaction with equal numbers of each type of atom on both sides of the equation. This balance demonstrates the conservation of mass, meaning atoms are neither created nor destroyed. For the burning of hydrogen:\[ 2H_2(g) + O_2(g) \rightarrow 2H_2O(l) \]This equation is balanced because:

• There are 4 hydrogen atoms on each side and 2 oxygen atoms on each side.

Balancing chemical equations ensures that the law of conservation of mass holds true. This also aids in accurate stoichiometry calculations, as proportions of reactants and products are crucial for predicting outcomes and ensuring reactions proceed correctly.