Problem 95 - Chemistry Matter and Change

Question

Oxygen Consumption If 5.00 L of hydrogen gas, measured at a temperature of 20.0°C and a pressure of 80.1 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

The mass of oxygen consumed when 5.00 L of hydrogen gas, measured at a temperature of 20.0°C and a pressure of 80.1 kPa, is burned in excess oxygen to form water is 3.44 g.

Step 1: Convert temperature to Kelvin

Given temperature is 20.0°C. To convert this to Kelvin: Temperature (K) = Temperature (°C) + 273.15 Temperature (K) = 20.0 + 273.15 = 293.15 K

Step 2: Calculate moles of hydrogen gas

Using the Ideal Gas Law (PV=nRT), n (H2) = PV / RT We need to convert pressure from kPa to atm: 80.1 kPa * (1 atm / 101.3 kPa) = 0.790 atm Now, use the given values and the gas constant (R = 0.08206 L.atm/(K.mol) ): n (H2) = (0.790 atm) * (5.00 L) / (0.08206 L.atm/(K.mol) * 293.15 K) n (H2) = 0.215 moles

Step 3: Calculate moles of oxygen consumed

Using the balanced chemical equation, 2 moles of H2 react with 1 mole of O2: 2 H2 + O2 -> 2 H2O n (O2) = (1/2) * n (H2) n (O2) = (1/2) * 0.215 moles = 0.1075 moles

Step 4: Calculate the mass of oxygen consumed

Using the molar mass of oxygen (16 g/mol for O, and 32 g/mol for O2): Mass (O2) = n (O2) * Molar mass (O2) Mass (O2) = 0.1075 moles * 32 g/mol = 3.44 g The mass of oxygen consumed in the reaction is 3.44 g.

Key Concepts

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in chemistry and physics. It allows us to relate pressure, volume, temperature, and the amount of gas in terms of moles. The equation is expressed as \( PV = nRT \), where:

• \( P \) stands for pressure.
• \( V \) is the volume.
• \( n \) represents the number of moles of gas.
• \( R \) is the ideal gas constant, commonly used as 0.08206 L.atm/(K.mol).
• \( T \) is the temperature in Kelvin.

When looking to solve problems using this law, a critical first step is ensuring all the values are in the correct units. Temperature, for example, must always be in Kelvin. To convert °C to Kelvin, simply add 273.15 to the Celsius temperature.
In the context of our exercise, the Ideal Gas Law helps calculate the number of moles of hydrogen present in a given volume of gas.

Chemical Reactions

Chemical reactions are processes where reactants transform into products. These reactions can usually be described with a balanced chemical equation, which shows the relationship between reactant and product molecules.
In our case, the reaction is between hydrogen gas (\( H_2 \)) and oxygen gas (\( O_2 \)) to produce water (\( H_2O \)). The balanced equation is:

• 2 \( H_2 \) + \( O_2 \) → 2 \( H_2O \)

This tells us that two moles of hydrogen react with one mole of oxygen to form two moles of water. The coefficients (numbers in front of the molecules) are crucial as they show the proportion in which elements react.
Understanding chemical reactions and how to balance them is fundamental for realizing the stoichiometry involved in calculating reactants and products.

Mole Calculations

Calculating moles is a core skill in chemistry. It allows us to quantify the amount of a substance using its chemical formula and the periodic table. A mole represents \(6.022 \times 10^{23}\) units of a substance, a number known as Avogadro's number.
To find the number of moles from a given mass, use the formula:

• \( n = \frac{m}{M} \)

where \( n \) is the number of moles, \( m \) is the mass, and \( M \) is the molar mass, typically in g/mol.
In the exercise, mole calculations were used twice: first, to determine the moles of hydrogen gas using the Ideal Gas Law, and second, to figure out how many moles of oxygen were consumed based on the stoichiometry of the chemical reaction.

Gas Laws

Gas laws are a collection of laws that describe the properties of gases and how they behave under different conditions.
The Ideal Gas Law is a combination of several simpler gas laws, such as Boyle's Law, Charles's Law, and Avogadro's Law:

• Boyle's Law states that pressure and volume are inversely proportional when temperature and moles are constant (\( PV = ext{constant} \)).
• Charles's Law says that volume and temperature are directly proportional under constant pressure and moles (\( V/T = ext{constant} \)).
• Avogadro's Law notes that volume and moles are directly proportional if pressure and temperature remain the same (\( V/n = ext{constant} \)).

These laws provide a basis for understanding the ideal behavior of gases. Although real gases may deviate under extreme conditions, these laws still give a useful approximation for predicting gas behavior in everyday scenarios. In the exercise, these principles underpin the calculations involving hydrogen and oxygen gases.