Question

Magnesium ribbon reacts with acid to produce hydrogen gas and magnesium ions. Different masses of magnesium ribbon are added to \(10 \mathrm{~mL}\) of the acid. The volume of the hydrogen gas obtained is a measure of the number of moles of hydrogen produced by the reaction. Various measurements are given in the table below.

Short answer

Answer: The relationship between the moles of magnesium ions produced and the moles of hydrogen gas produced in this reaction is a 1:1 ratio. This means the number of moles of magnesium ions produced is equal to the number of moles of hydrogen gas produced.

Step-by-step solution

Understand the chemical reaction

The chemical reaction involved in this exercise is between magnesium ribbon and an acid. When magnesium reacts with an acid, it produces hydrogen gas and magnesium ions. The balanced equation for the reaction is: $$\mathrm{Mg} + 2\mathrm{H^+} \to \mathrm{Mg^{2+}} + \mathrm{H_2}$$ Inspecting the equation can help understand the stoichiometry of the reaction and how it relates to the number of moles of hydrogen produced.

Examine the given data

Since the problem provides a table with different measurements, it is important to carefully examine the data. This table likely contains information such as the mass of magnesium ribbon used, the volume of the acid, and the volume of hydrogen gas produced. Take note of the values and units given in the table, and ensure the data is organized clearly to facilitate further analysis.

Moles of hydrogen produced

To connect the volume of hydrogen gas with the number of moles produced, the ideal gas law can be used. The ideal gas law states: $$PV = nRT$$ where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant and T is the temperature. Working with the assumption that the reaction takes place at constant temperature and pressure, we can use the volume of hydrogen gas produced to calculate the number of moles of hydrogen in each scenario. To do this, rearrange the ideal gas law to solve for moles: $$n = \frac{PV}{RT}$$ Obtain the values for P, V, R, and T from the given data or constants, and calculate the moles of hydrogen gas produced in each case.

Moles of magnesium ions

The next step is to find the moles of magnesium ions based on the balanced chemical equation. As seen in Step 1, there is a 1:1 ratio between the moles of magnesium and the moles of hydrogen. Thus, the number of moles of magnesium ions produced (n_Mg) is equal to the number of moles of hydrogen produced (n_H2): $$n_{\mathrm{Mg}} = n_{\mathrm{H_2}}$$ Use the moles of hydrogen calculated in Step 3 to determine the moles of magnesium ions.

Understanding the reaction ratios

With the number of moles of magnesium ions and hydrogen gas calculated, the next step is to analyze any relationships or trends in the data. For instance, exploring how the mass of magnesium ribbon affects the moles of hydrogen produced, or the effect of different volumes of acid on the reaction. Take note of the mass of magnesium used and the moles of hydrogen produced to make conclusions about the mass ratio, and potentially observe any connections or patterns in the data. Ultimately, the goal is to help the student understand the reaction ratios and stoichiometry, and to be able to apply that knowledge in interpreting the provided data. By following these steps, the student will have a better grasp of the problem and will be ready to tackle similar exercises.