To determine how many moles of hydrochloric acid (HCl) reacted with magnesium, we can follow these steps:
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Calculate the number of moles of hydrochloric acid: The concentration of hydrochloric acid is given as 0.2 M (moles per liter). The volume of the hydrochloric acid solution is given as 100 cm³, which can be converted to liters:
\[ 100 , \text{cm}^3 = 0.100 , \text{L} \]
Now we can calculate the number of moles of hydrochloric acid:
\[ \text{moles of HCl} = \text{concentration} \times \text{volume} = 0.2 , \text{mol/L} \times 0.100 , \text{L} = 0.020 , \text{mol} \]
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Calculate the number of moles of magnesium: The molar mass of magnesium (Mg) is approximately 24.31 g/mol. We can calculate the number of moles of magnesium:
\[ \text{moles of Mg} = \frac{\text{mass}}{\text{molar mass}} = \frac{0.12 , \text{g}}{24.31 , \text{g/mol}} \approx 0.00493 , \text{mol} \]
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Determine the reaction of magnesium with hydrochloric acid: The balanced chemical reaction between magnesium and hydrochloric acid is:
\[ \text{Mg} + 2\text{HCl} \rightarrow \text{MgCl}_2 + \text{H}_2 \]
From the balanced equation, we see that 1 mole of magnesium reacts with 2 moles of hydrochloric acid. Therefore, the number of moles of hydrochloric acid required to react with the magnesium we have can be calculated as:
\[ \text{moles of HCl required} = 2 \times \text{moles of Mg} = 2 \times 0.00493 , \text{mol} \approx 0.00986 , \text{mol} \]
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Determine how many moles of hydrochloric acid reacted: Since we have 0.020 mol of HCl available, and only approximately 0.00986 mol is required to fully react with the available magnesium, the hydrochloric acid that actually reacted is 0.00986 mol.
Thus, the moles of hydrochloric acid that reacted with magnesium is approximately 0.00986 moles.