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[tex]$40.0 \, \text{mL}$[/tex] of [tex]$1.0 \, \text{M HCl}$[/tex] is added to a coffee cup. Then [tex]$0.486 \, \text{g Mg}$[/tex] are added. What is the mass of the solution?

[tex]\[
\begin{array}{c}
d_{\text{HCl}} = 1.02 \, \text{g/mL} \\
\text{Mass}_{\text{HCl}} = \frac{40.0 \, \text{mL}}{1} \times \frac{1.02 \, \text{g}}{\text{mL}} = 40.8 \, \text{g} \\
\text{Mass}_{\text{soln}} = 40.8 \, \text{g} + 0.486 \, \text{g}
\end{array}
\][/tex]



Answer :

GinnyAnswer
To determine the mass of the solution, let's break the problem down into clear steps, using the given data:

1. Determine the volume and density of hydrochloric acid (HCl):
- Volume of HCl: \( 40.0 \) mL
- Density of HCl: \( 1.02 \) g/mL

2. Calculate the mass of hydrochloric acid (HCl):
- Mass of HCl can be calculated by multiplying its volume by its density.
[tex]\[ \text{Mass}_{\text{HCl}} = \text{Volume}_{\text{HCl}} \times \text{Density}_{\text{HCl}} \][/tex]
Substituting the given values:
[tex]\[ \text{Mass}_{\text{HCl}} = 40.0 \text{ mL} \times 1.02 \text{ g/mL} = 40.8 \text{ g} \][/tex]

3. Given the mass of magnesium (Mg) added:
- Mass of Mg: \( 0.486 \) g

4. Calculate the total mass of the solution:
- The total mass of the solution is the sum of the mass of HCl and the mass of Mg.
[tex]\[ \text{Mass}_{\text{solution}} = \text{Mass}_{\text{HCl}} + \text{Mass}_{\text{Mg}} \][/tex]
Substituting the values we have:
[tex]\[ \text{Mass}_{\text{solution}} = 40.8 \text{ g} + 0.486 \text{ g} = 41.286 \text{ g} \][/tex]

Thus, the mass of the solution is [tex]\( 41.286 \)[/tex] g.

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