To determine the mass/mass percent ([tex]\( m/m \% \)[/tex]) of [tex]\( \text{Na}_2\text{CO}_3 \)[/tex] in the solution, follow these steps:
1. Identify the given values:
- Mass of [tex]\( \text{Na}_2\text{CO}_3 \)[/tex] = 43.5 grams
- Mass of the total solution = 227.0 grams
2. Calculate the mass/mass percent:
The mass/mass percent ([tex]\( m/m \% \)[/tex]) is calculated using the formula:
[tex]\[
\text{Mass/ Mass Percent} = \left( \frac{\text{Mass of solute}}{\text{Mass of solution}} \right) \times 100
\][/tex]
Substituting the given values:
[tex]\[
m/m \% = \left( \frac{43.5 \, \text{g}}{227.0 \, \text{g}} \right) \times 100
\][/tex]
3. Perform the division:
First, divide the mass of the solute by the mass of the solution:
[tex]\[
\frac{43.5}{227.0} \approx 0.19163
\][/tex]
4. Multiply by 100 to get the percentage:
[tex]\[
0.19163 \times 100 = 19.163
\][/tex]
5. Round your answer to two significant figures:
When rounding 19.163 to two significant figures:
[tex]\[
19.16 \% \approx 19 \%
\][/tex]
So, the mass/mass percent ([tex]\( m/m \% \)[/tex]) of [tex]\( \text{Na}_2\text{CO}_3 \)[/tex] in the solution, expressed to two significant figures, is:
[tex]\[
\boxed{19.16 \%}
\][/tex]
