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Chapter 12: Problem 206

A \(50.00\) -mL sample of hydrochloric acid of unknown concentration was neutralized by \(47.35 \mathrm{~mL}\) of \(0.01020 \mathrm{M}\) sodium hydroxide solution. Calculate the concentration of the original HCl solution.

Short Answer

Expert verified
The concentration of the original HCl solution is approximately \(0.00966 \mathrm{M}\).

Step by step solution

01

The balanced chemical equation for the neutralization of hydrochloric acid (HCl) by sodium hydroxide (NaOH) is: \( HCl + NaOH \rightarrow NaCl + H_2O \) Since it's a one-to-one reaction, the number of moles of HCl is equal to the number of moles of NaOH when they completely react with each other. #Step 2: Determine the moles of NaOH used in the reaction#

We are given the concentration of NaOH (0.01020 M) and the volume used (47.35 mL). We can now find the moles of NaOH using the relation: moles of NaOH = concentration × volume But first, let's convert the volume of NaOH solution from milliliters (mL) to liters (L) as the concentration is given in moles per liter: \[ V_{NaOH} (\text{L}) = 47.35 \times \frac{1}{1000} = 0.04735 \] Now, find the moles of NaOH: \[ \text{moles of NaOH} = 0.01020 \times 0.04735 = 0.000483 \] So, 0.000483 mol of NaOH were used to neutralize the HCl solution. #Step 3: Calculate the moles of HCl in the reaction#
02

As discussed earlier, the number of moles of HCl is equal to the number of moles of NaOH when they react: moles of HCl = moles of NaOH So, 0.000483 mol of HCl are present in the 50.00-mL sample. #Step 4: Calculate the concentration of HCl in the original solution#

Now, we can use the moles of HCl and the given volume of HCl solution (50.00 mL) to find the concentration using the formula: \[ c_{HCl} = \frac{\text{moles of HCl}}{V_{HCl} (\text{L})} \] But first, like earlier, let's convert the volume of the HCl solution from milliliters (mL) to liters (L): \[ V_{HCl} (\text{L}) = 50.00 \times \frac{1}{1000} = 0.05000 \] Now, find the concentration of HCl: \[ c_{HCl} = \frac{0.000483}{0.05000} = 0.00966 \] So, the concentration of the original HCl solution is approximately 0.00966 M.

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