Question

check your volume measurement. did you report your data to the correct number of significant figures? concentration of hydrochloric acid (m) 2.11 concentration of sodium hydroxide (m) 2.05 calorimeter constant (j/°c) 13.4 volume of hydrochloric acid (ml) 93.0 temperature of hydrochloric acid (°c) 24.0 volume of sodium hydroxide (ml) temperature of sodium hydroxide (°c) 24.0 final temperature after mixing (°c) 37.8

Explanation:

To determine the volume of sodium hydroxide, we can use the concept of stoichiometry for the neutralization reaction between HCl and NaOH: \( \text{HCl} + \text{NaOH}
ightarrow \text{NaCl} + \text{H}_2\text{O} \). At the equivalence point, the moles of HCl equal the moles of NaOH.

Step 1: Calculate moles of HCl

The formula for moles (\( n \)) is \( n = C \times V \), where \( C \) is concentration (in mol/L or M) and \( V \) is volume (in L).
First, convert the volume of HCl to liters: \( V_{\text{HCl}} = 93.0 \, \text{mL} = \frac{93.0}{1000} \, \text{L} = 0.0930 \, \text{L} \).
Moles of HCl: \( n_{\text{HCl}} = C_{\text{HCl}} \times V_{\text{HCl}} = 2.11 \, \text{M} \times 0.0930 \, \text{L} \).
\( n_{\text{HCl}} = 2.11 \times 0.0930 = 0.19623 \, \text{mol} \).

Step 2: Moles of NaOH (equivalence point)

At neutralization, \( n_{\text{NaOH}} = n_{\text{HCl}} = 0.19623 \, \text{mol} \).

Step 3: Calculate volume of NaOH

Using \( V = \frac{n}{C} \), where \( C_{\text{NaOH}} = 2.05 \, \text{M} \).
\( V_{\text{NaOH}} = \frac{n_{\text{NaOH}}}{C_{\text{NaOH}}} = \frac{0.19623 \, \text{mol}}{2.05 \, \text{M}} \).
\( V_{\text{NaOH}} = \frac{0.19623}{2.05} \approx 0.095722 \, \text{L} \).
Convert back to milliliters: \( V_{\text{NaOH}} = 0.095722 \, \text{L} \times 1000 = 95.722 \, \text{mL} \).

Now, check significant figures:

• \( C_{\text{HCl}} = 2.11 \) (3 sig figs), \( V_{\text{HCl}} = 93.0 \) (3 sig figs), \( C_{\text{NaOH}} = 2.05 \) (3 sig figs).
• The least number of decimal places in multiplication/division is determined by sig figs. All values have 3 sig figs, so the result should have 3 sig figs.

Rounding \( 95.722 \, \text{mL} \) to 3 sig figs: \( 95.7 \, \text{mL} \) (or check if more precise: \( 95.7 \, \text{mL} \) is 3 sig figs).

Answer:

The volume of sodium hydroxide is approximately \( \boldsymbol{95.7 \, \text{mL}} \) (or \( 95.7 \) when reported to 3 significant figures, consistent with the data provided).