Question

A solid sample of \(\mathrm{Zn}(\mathrm{OH})_{2}\) is added to \(0.350 \mathrm{~L}\) of \(0.500\) \(M\) aqueous HBr. The solution that remains is still acidic. It is then titrated with \(0.500 \mathrm{M} \mathrm{NaOH}\) solution, and it takes \(88.5 \mathrm{~mL}\) of the \(\mathrm{NaOH}\) solution to reach the equivalence point. What mass of \(\mathrm{Zn}(\mathrm{OH})_{2}\) was added to the HBr solution?

Short answer

The mass of Zn(OH)₂ added to the HBr solution is approximately 6.50 g.

Step-by-step solution

Calculate initial moles of HBr

First, we need to find the number of moles of HBr initially present in the solution. To do this, we can use the given concentration and volume of HBr: moles of HBr = (concentration of HBr) × (volume of HBr solution) moles of HBr = (0.500 M) × (0.350 L) = 0.175 mol

Calculate moles of HBr remaining after titration

Since the solution is still acidic when titrated with NaOH, we can use the volume and concentration of NaOH to find the number of moles of HBr remaining after the reaction: moles of HBr remaining = (concentration of NaOH) × (volume of NaOH solution) moles of HBr remaining = (0.500 M) × (0.0885 L) = 0.04425 mol

Calculate moles of HBr reacted with Zn(OH)₂

Now, we can find the number of moles of HBr reacted with Zn(OH)₂ by subtracting the remaining moles of HBr from the initial moles of HBr: moles of HBr reacted = initial moles of HBr - moles of HBr remaining moles of HBr reacted = 0.175 mol - 0.04425 mol = 0.13075 mol

Calculate moles of Zn(OH)₂

The balanced chemical equation for the reaction between Zn(OH)₂ and HBr is: Zn(OH)₂ + 2HBr → ZnBr₂ + 2H₂O From the balanced equation, we can see that 1 mole of Zn(OH)₂ reacts with 2 moles of HBr. So, we can find the number of moles of Zn(OH)₂ that reacted with HBr: moles of Zn(OH)₂ = moles of HBr reacted / 2 moles of Zn(OH)₂ = 0.13075 mol / 2 = 0.065375 mol

Calculate mass of Zn(OH)₂

Finally, we can calculate the mass of Zn(OH)₂ using its molar mass (Zn: 65.38 g/mol, O: 16.00 g/mol, H: 1.01 g/mol): molar mass of Zn(OH)₂ = 65.38 g/mol + 2(16.00 g/mol + 1.01 g/mol) = 99.40 g/mol mass of Zn(OH)₂ = moles of Zn(OH)₂ × molar mass of Zn(OH)₂ mass of Zn(OH)₂ = 0.065375 mol × 99.40 g/mol ≈ 6.50 g Thus, about 6.50 g of Zn(OH)₂ was added to the HBr solution.

Key concepts

Acid-Base Titration

Acid-base titration is a method in chemistry used to determine the concentration of an acidic or basic solution. It involves adding a base (or acid) of known concentration to an acid (or base) of unknown concentration until the reaction reaches the equivalence point. At this point, the amount of acid equals the amount of base, indicating neutralization has been achieved.

In the process of titration, indicators or pH meters are often used to detect the endpoint. The endpoint is indicated by a noticeable change, which is often visible through a color shift if an indicator dye is used.

In the given exercise, the NaOH solution acts as the titrant used to titrate the acidic solution of HBr leftover after the reaction with Zn(OH) substance{2}. You measure the volume of NaOH added to reach neutrality. Doing so provides the data to calculate how much HBr reacted. This step is critical to determining how much substance{Zn(OH)} substance{2} was initially present.

Molar Mass Calculation

Molar mass is a fundamental concept in stoichiometry, crucial for converting between the mass of a substance and the number of moles. This calculation is achieved by summing the atomic masses of each element present in a compound.

In the exercise, we calculate the molar mass of Zn(OH) substance{2}. Here's how it works:

• Zinc (Zn) contributes 65.38 g/mol.
• Oxygen (O) has an atomic mass of 16.00 g/mol. Two oxygen atoms make it 32.00 g/mol.
• Hydrogen (H) is 1.01 g/mol, and with two hydrogen atoms, it sums to 2.02 g/mol.

The total molar mass of Zn(OH) substance{2} is thus calculated as 65.38 g/mol (for Zn) + 32.00 g/mol (for O) + 2.02 g/mol (for H) = 99.40 g/mol.

Understanding molar mass allows for the translation of observed weights in lab experiments to the more abstract and universally applicable concept of moles. This insight is used to measure reactants and predict products accurately in chemical reactions.

Chemical Reactions

A chemical reaction involves the conversion of reactants into products. It's represented by a balanced chemical equation, which shows the number of each atom is conserved as reactions proceed.

For the exercise at hand, the reaction involves the neutralization of an acid by a base, demonstrated in the equation:
Zn(OH) substance{2} + 2 HBr → ZnBr substance{2} + 2 H substance{2}O (water)

This means one mole of zinc hydroxide reacts with two moles of hydrobromic acid to produce one mole of zinc bromide and two moles of water. Understanding this stoichiometric ratio is crucial for calculating how different quantities of substances interact during reactions.

This balanced equation helps predict the yield of a reaction, thus allowing chemists to determine how much reactant is needed or how much product will be formed. So, in the exercise, knowing the amount of HBr that reacted with Zn(OH) substance{2} helps calculate how much Zn(OH) substance{2} was originally added.