Let’s calculate the mass percent (m/m) of a solution where we dissolve 54.21 grams of NaCl (sodium chloride) in 153.9 grams of H₂O (water). We will express the final mass percent to four significant figures.
### Step-by-Step Solution:
1. Determine the total mass of the solution:
The total mass of the solution is the sum of the mass of NaCl and the mass of H₂O.
[tex]\[
\text{Total mass of solution} = \text{mass of NaCl} + \text{mass of H₂O}
\][/tex]
Substituting the given values:
[tex]\[
\text{Total mass of solution} = 54.21 \, \text{g} + 153.9 \, \text{g} = 208.11 \, \text{g}
\][/tex]
2. Calculate the mass percent (m/m):
The mass percent (m/m) is calculated using the formula:
[tex]\[
\text{Mass percent} = \left( \frac{\text{mass of solute (NaCl)}}{\text{total mass of solution}} \right) \times 100
\][/tex]
Plugging in the known values:
[tex]\[
\text{Mass percent} = \left( \frac{54.21 \, \text{g}}{208.11 \, \text{g}} \right) \times 100
\][/tex]
Evaluating this expression:
[tex]\[
\text{Mass percent} \approx 26.048724232377108
\][/tex]
3. Round the mass percent to four significant figures:
For clarity and precision, we round our result to four significant figures:
[tex]\[
\text{Mass percent (rounded)} \approx 26.0487 \, \%
\][/tex]
Therefore, the mass percent (m/m) of the solution prepared by dissolving 54.21 g of NaCl in 153.9 g of H₂O, expressed to four significant figures, is:
[tex]\[
26.0487 \, \%
\][/tex]
