Problem 91 - Chemistry The Molecular Science

Question

Diborane, \(\mathrm{B}_{2} \mathrm{H}_{6},\) can be produced by this reaction: \(2 \mathrm{NaBH}_{4}(\mathrm{~s})+\mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{aq}) \longrightarrow\) \(2 \mathrm{H}_{2}(\mathrm{~g})+\mathrm{Na}_{2} \mathrm{SO}_{4}(\mathrm{aq})+\mathrm{B}_{2} \mathrm{H}_{6}(\mathrm{~g})\) Calculate the volume, in milliliters, of \(0.0875-\mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\) needed to completely react with \(1.35 \mathrm{~g} \mathrm{NaBH}_{4}\)..

Step-by-Step Solution

Answer

33.9 mL of 0.0875-M H2SO4 is needed.

Step 1: Determine Moles of NaBH4

First, calculate the moles of sodium borohydride (\(\text{NaBH}_4\)) using its given mass and molar mass. The molar mass of\[\text{NaBH}_4 = 23 + 10.8 \times 4 + 1 \times 4 = 37.83\,\text{g/mol}\].Given mass = 1.35 g, so the number of moles of \(\text{NaBH}_4\) is:\[\frac{1.35\,\text{g}}{37.83\,\text{g/mol}} = 0.0357\,\text{moles}\].

Key Concepts

Molar Mass Calculation

Calculating the molar mass of a compound is a foundational step in chemistry, especially when dealing with chemical reactions. It allows us to understand how much of each element is present in a compound by weight. To calculate the molar mass, you need to sum up the atomic masses of all the atoms in a molecule.
Here’s a simple guide:

• Identify the elements in the compound and their respective numbers. For example, in sodium borohydride (\(\text{NaBH}_4\)), the elements are sodium (Na), boron (B), and hydrogen (H).
• Look up the atomic masses from the periodic table: Na = 23 g/mol, B = 10.8 g/mol, and H = 1 g/mol.
• Multiply each element's atomic mass by the number of atoms in the compound and then add the totals to get the molar mass: \[23\, \text{g/mol} + (10.8\,\text{g/mol} \times 4) + (1\,\text{g/mol} \times 4) = 37.83\,\text{g/mol}\]

This molar mass allows us to convert between grams and moles, which is critical for stoichiometry calculations.

Stoichiometry

Stoichiometry is a key concept in chemistry that helps us quantify the relationships between reactants and products in a chemical reaction. By using the balanced chemical equation, we can predict how much product will result from certain amounts of reactants. For the reaction given, balance the equation:\(2 \text{NaBH}_4 + \text{H}_2\text{SO}_4 \rightarrow 2 \text{H}_2 + \text{Na}_2\text{SO}_4 + \text{B}_2\text{H}_6\).
Here's how stoichiometry works:

• Use the coefficients in the balanced equation to determine the mole ratio between reactants and products. In our example: - 2 moles of NaBH₄ react with 1 mole of H₂SO₄.
• Based on the calculated moles of NaBH₄ (0.0357 moles), use the mole ratio to find the moles of H₂SO₄ needed: - 0.0357 moles NaBH₄ × (1 mole H₂SO₄ / 2 moles NaBH₄) = 0.01785 moles H₂SO₄.

This shows how stoichiometry bridges the gap between reactants and the products they form in chemical reactions.

Solution Concentration

Understanding the concentration of a solution is essential in many chemical calculations. Concentration is typically expressed as molarity, which is the number of moles of solute per liter of solution. For our exercise, we need to find how much of the \(0.0875 \text{-M H}_2 \text{SO}_4\) solution is required.
Here’s how you can connect concentration with your chemical calculations:

• Since molarity is moles per liter (\( ext{M} = \text{mol/L}\)), to find the volume in liters of 0.0875 M H₂SO₄, use the relation: \[\text{Volume} = \frac{\text{moles of solute}}{\text{molarity}}\]
• For our calculated 0.01785 moles of H₂SO₄, \[\text{Volume} = \frac{0.01785 \text{ moles}}{0.0875 \text{ mol/L}} = 0.204 L\]
• Convert the volume from liters to milliliters: \(0.204 \text{ L} = 204 \text{ mL}\).

This makes it easier to visualize the amount of solution needed for the reaction.