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Balanced Chemical Equation:

[tex]\[ \text{Mg} + 2 \text{AgNO}_3 \rightarrow 2 \text{Ag} + \text{Mg}(\text{NO}_3)_2 \][/tex]

What conversion goes in the green boxes?

[tex]\[
\begin{array}{l}
\begin{array}{l|l|l|l}
48 \, \text{g} \, \text{Mg} & 1 \, \text{mol} \, \text{Mg} & 2 \, \text{mol} \, \text{Ag} & \left[ ? \right] \\
\hline
& 24 \, \text{g} \, \text{Mg} & 1 \, \text{mol} \, \text{Ag} & \left[ ? \right]
\end{array} \, = \, ? \, \text{g} \, \text{Ag} \\
\frac{1 \, \text{mol} \, \text{Mg}}{24 \, \text{g} \, \text{Mg}} \\
\frac{2 \, \text{mol} \, \text{Ag}}{1 \, \text{mol} \, \text{Mg}} \\
\frac{108 \, \text{g} \, \text{Ag}}{1 \, \text{mol} \, \text{Ag}} \\
\end{array}
\][/tex]

Calculate the mass of silver (Ag) produced.



Answer :

GinnyAnswer
Let's go through this problem step-by-step:

1. Convert grams of Mg to moles of Mg:
- Given: [tex]\(48\)[/tex] grams of [tex]\(Mg\)[/tex].
- Molar mass of magnesium ([tex]\(Mg\)[/tex]) is [tex]\(24 \text{ g/mol}\)[/tex].

[tex]\[ \text{Moles of } Mg = \frac{\text{grams of } Mg}{\text{molar mass of } Mg} = \frac{48 \text{ g}}{24 \text{ g/mol}} = 2 \text{ mol} \][/tex]

2. Use the stoichiometry of the reaction:
- The balanced chemical equation is:
[tex]\[ Mg + 2AgNO_3 \rightarrow 2Ag + Mg(NO_3)_2 \][/tex]
- According to the equation, [tex]\(1 \text{ mole of } Mg\)[/tex] produces [tex]\(2 \text{ moles of } Ag\)[/tex].

[tex]\[ \text{Moles of } Ag = 2 \text{ moles of } Mg \times 2 = 4 \text{ moles of } Ag \][/tex]

3. Convert moles of Ag to grams of Ag:
- Molar mass of silver ([tex]\(Ag\)[/tex]) is [tex]\(108 \text{ g/mol}\)[/tex].

[tex]\[ \text{Grams of } Ag = \text{moles of } Ag \times \text{molar mass of } Ag = 4 \text{ moles} \times 108 \text{ g/mol} = 432 \text{ g} \][/tex]

4. Fill in the green boxes in the conversion grid:

[tex]\[ \begin{array}{l} \begin{array}{l|l|l|l} 48 \text{ g Mg} & 1 \text{ mol Mg} & 2 \text{ mol Ag} & 432 \text{ g Ag} \\ \hline & 24 \text{ g Mg} & 1 \text{ mol Mg} & 108 \text{ g Ag} \end{array} = 432 \text{ g Ag} \end{array} \][/tex]

So, the numerical result for the final product is [tex]\(432 \text{ g Ag}\)[/tex]. The conversion values matter and confirm that 48 grams of [tex]\(Mg\)[/tex] reacts to yield 432 grams of [tex]\(Ag\)[/tex].

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