Question

Calcium metal reacts with water to produce hydrogen gas. The gas displaces water from a graduated cylinder, and the water level decreases from \(75.5 \mathrm{~mL}\) to \(43.0 \mathrm{~mL}\). What is the volume of gas produced by the reaction?

Short answer

The volume of hydrogen gas produced is 32.5 mL.

Step-by-step solution

Understand the Reaction

The chemical reaction between calcium metal and water produces hydrogen gas and calcium hydroxide: \( \text{Ca (s)} + 2\text{H}_2\text{O (l)} \rightarrow \text{Ca(OH)}_2\text{(aq)} + \text{H}_2 (g) \). Our focus is on determining the volume of hydrogen gas produced, which directly corresponds to the decrease in the volume of water.

Measure Initial and Final Volumes

Review the initial and final volumes of water in the graduated cylinder. Initially, the water level was \(75.5 \mathrm{~mL}\). After the reaction and displacement of water by the hydrogen gas, the water level decreased to \(43.0 \mathrm{~mL}\).

Calculate Change in Volume

Determine the change in volume by subtracting the final volume of water from the initial volume. This gives the volume of the gas produced. Use the formula: \( V_{\text{gas}} = V_{\text{initial}} - V_{\text{final}} \), where \( V_{\text{initial}} = 75.5 \mathrm{~mL} \) and \( V_{\text{final}} = 43.0 \mathrm{~mL} \).

Perform the Calculation

Calculate the volume of the gas produced using the values from Step 3: \( V_{\text{gas}} = 75.5 \mathrm{~mL} - 43.0 \mathrm{~mL} = 32.5 \mathrm{~mL} \).

Conclusion

The volume of hydrogen gas produced by the reaction is \(32.5 \mathrm{~mL}\). This is the volume of gas that displaced the equivalent amount of water.

Key concepts

Stoichiometry

Stoichiometry is like a recipe for chemical reactions. It helps you predict and understand the quantities of all substances involved. When calcium reacts with water, a balanced chemical equation shows that one mole of calcium reacts with two moles of water to produce one mole of hydrogen gas and one mole of calcium hydroxide. Knowing the ratio of reactants to products is crucial. It helps us determine how much product is made from a given amount of reactant. In our exercise, the reaction is represented by the equation:

• \( \text{Ca (s)} + 2\text{H}_2\text{O (l)} \rightarrow \text{Ca(OH)}_2\text{(aq)} + \text{H}_2 (g) \).

The stoichiometric coefficients (numbers in front of the chemical formulas) tell us how many atoms or molecules take part in the reaction. These help us to maintain a balance between reactants and products in terms of atoms and mass. Stoichiometry ensures that no atoms are lost or gained but merely reorganized, adhering to the law of conservation of mass.
Thus, stoichiometry gives us a mathematical framework to calculate how much hydrogen gas is produced when a known amount of calcium reacts.

Gas Displacement

Gas displacement is a clever method to collect and measure the gas produced from a chemical reaction. In our exercise, hydrogen gas is collected by displacing water in a graduated cylinder. This works because the gas is less dense and less soluble in water, pushing the water level down as more gas enters the cylinder.
The idea here is that the volume of gas produced is equal to the volume of the liquid displaced. As seen in the problem, the initial water level was at 75.5 mL, and after the reaction, it went down to 43.0 mL. The change in volume gives us the amount of gas that was produced, which in this case, is 32.5 mL.
Using the gas displacement method makes measuring gases more manageable, especially when dealing with gasses that are transparent and hard to grasp through other means.

Volume Measurement

Volume measurement is vital when determining the amount of gas produced in reactions. Here, we use a graduated cylinder to find out how much hydrogen gas is formed by observing the displacement of water. The graduated cylinder allows precise measurements of the water before and after the reaction.
Initial measurements are usually made before starting the reaction. In our example, the water level starts at 75.5 mL. After the reaction is complete, a new measurement is taken, showing the water level at 43.0 mL. By subtracting the final volume from the initial volume, we can precisely calculate the volume of the hydrogen gas produced:

• Initial water level: 75.5 mL
• Final water level: 43.0 mL
• Volume of hydrogen gas produced: \(75.5 - 43.0 = 32.5 \text{ mL}\)

This simple subtraction allows us to quantify the gas released through the reaction accurately. Volume measurement thus plays a crucial role in experimental chemistry, where accuracy and precision are vital.