To determine the concentration of a solute in a solvent, we use the following equation:
[tex]\[
\text{Concentration} = \frac{\text{Mass of solute}}{\text{Volume of solvent}}
\][/tex]
Given the problem details:
- Mass of solute, [tex]\(m_{\text{solute}} = 0.078 \, \text{g}\)[/tex]
- Volume of solvent, [tex]\(V_{\text{solvent}} = 0.100 \, \text{mL}\)[/tex] (since [tex]\(1 \, \text{g} \, \text{H}_2\text{O} = 1 \, \text{mL} \, \text{H}_2\text{O}\)[/tex])
Using the equation for concentration:
[tex]\[
\text{Concentration} = \frac{0.078 \, \text{g}}{0.100 \, \text{mL}}
\][/tex]
Performing the division gives:
[tex]\[
\text{Concentration} = 0.78 \, \text{g/mL}
\][/tex]
So, the concentration of the solute in the solvent at [tex]\(20.5^\circ \text{C}\)[/tex] is:
[tex]\[
\boxed{0.780 \, \text{g/mL}}
\][/tex]
