Question

Analysis shows that a sample of \(\mathrm{H}_{2} \mathrm{X}(\mathrm{MM}=100.0 \mathrm{~g} / \mathrm{mol})\) reacts completely with \(330.0 \mathrm{~mL}\) of \(0.2000 \mathrm{M} \mathrm{KOH}\). $$\mathrm{H}_{2} \mathrm{X}(a q)+2 \mathrm{OH}^{-}(a q) \longrightarrow \mathrm{X}^{2-}(a q)+2 \mathrm{H}_{2} \mathrm{O}$$ What is the volume of the sample? (Density of \(\mathrm{H}_{2} \mathrm{X}=\) \(1.200 \mathrm{~g} / \mathrm{mL}\).)

Short answer

Question: Determine the volume of the sample of an unknown compound H2X when it reacts completely with 330.0 mL of 0.2000 M KOH solution. The molar mass of H2X is 100.0 g/mol, and its density is 1.200 g/mL. Answer: The volume of the sample of H2X is 2.75 mL.

Step-by-step solution

Calculate the moles of OH−

Since we know the volume and concentration of KOH solution, we can determine the moles of OH- ions. Recall the equation: moles = volume × concentration. The volume of KOH solution is 330.0 mL (convert to liters by dividing by 1000): $$\frac{330.0}{1000} = 0.330 \mathrm{~L}$$ Now, use the given concentration to find the moles of OH- ions: $$\text{moles of OH-} = 0.2000\mathrm{M} \times 0.330\mathrm{~L} = 0.0660\mathrm{~mol\; OH-}$$

Calculate the moles of H2X

Now that we know the moles of OH- in the reaction, we can use the stoichiometric coefficients in the balanced chemical equation to determine the moles of H2X reacting with it. Notice that the stoichiometric ratio between H2X and OH- is 1:2. Therefore, for every 2 moles of OH- ions, there is 1 mole of H2X. Using this ratio, we can calculate the moles of H2X in the reaction: $$\text{moles of H2X} = \frac{1}{2} \times 0.0660\mathrm{~mol\; OH-} = 0.0330\mathrm{~mol\; H2X}$$

Calculate the mass of H2X

Now that we know the moles of H2X, we can convert it into mass (in grams) using the given molar mass of H2X (100.0 g/mol): $$\text{mass of H2X} = 0.0330\mathrm{~mol\; H2X} \times 100.0\mathrm{~g/mol} = 3.30\mathrm{~g\; H2X}$$

Calculate the volume of H2X

Finally, we will calculate the volume of H2X using its mass and the given density. Recall the equation: Density = mass/volume Rearranging, we can calculate the volume as: $$\text{volume} = \frac{\text{mass}}{\text{density}}$$ Substitute the mass of H2X (3.30 g) and the given density of H2X (1.200 g/mL): $$\text{volume} = \frac{3.30\mathrm{~g}}{1.200\mathrm{~g/mL}} = 2.75\mathrm{~mL}$$ The volume of the sample of H2X is 2.75 mL.

Key concepts

Chemical Reaction Calculation

Understanding a chemical reaction often starts with a balanced chemical equation, which provides a recipe for the reactants and products involved in the reaction. In the context of stoichiometry, the coefficients in a balanced equation indicate the ratios at which substances react and form products. This is crucial for determining how much of each reactant you need and how much of each product you can expect to produce.

For example, the balanced equation in our exercise is: \[\text{H}_2\text{X} + 2\text{OH}^- \rightarrow \text{X}^{2-} + 2\text{H}_2\text{O}\]
It shows that one molecule of \(\text{H}_2\text{X}\) reacts with two hydroxide ions (\(\text{OH}^-\)) to produce one ion of \(\text{X}^{2-}\) and two molecules of water. To calculate the amount of reactants needed or products formed, you must firstly understand the concept of moles, which leads us neatly into our next section on the mole concept.

Mole Concept

The mole is a fundamental unit in chemistry that provides a bridge between the atomic and macroscopic worlds. One mole is defined as the amount of a substance that contains as many entities (atoms, molecules, ions, etc.) as there are atoms in 12 grams of carbon-12. This number is Avogadro's number, approximately \(6.022 \times 10^{23}\).

In practical terms, the mole concept allows chemists to count particles by weighing them. It's used to convert between the mass of a substance and the amount of substance in moles, as was necessary in our exercise above. By knowing the molar mass of \(\text{H}_2\text{X}\), we could determine the number of moles from its mass and further connect it to the volume of the solution using the concept of solution concentration.

Solution Concentration

Solution concentration describes how much of a substance, known as the solute, is dissolved in a given volume of solvent. There are various ways to express concentration, but molarity (M) is one of the most common, especially in a laboratory setting. Molarity is defined as the number of moles of solute per liter of solution.

In our exercise, the concentration of KOH solution was given as 0.2000 M. This means for every liter of solution, there are 0.2000 moles of \(\text{KOH}\). From here, we used the volume of the KOH solution to calculate the moles of hydroxide ions, \(\text{OH}^-\), as they are central to the entire reaction. By understanding how concentration relates to the amount of reactants in a chemical equation, you can tackle a wide range of stoichiometry problems, such as finding the volume of a reactant or product, as done in the final step of our exercise.