Magnesium metal reacts with dilute hydrochloric acid to produce magnesium chloride and hydrogen. The chemical equation for the reaction is shown below.
[tex]Mg(s)+2 HCl(aq) \longrightarrow MgCl_2(aq)+H_2(g)[/tex]
Starting with the known mass, 12.0 g of Mg, calculate the following:
(a) the mass of HCl reacted,
(b) the mass of [tex]MgCl_2[/tex] produced ([tex]Mg =24, Cl =35.5, H =1[/tex]).
Answer (2)
Calculate the number of moles of Mg: n M g = 24 g / m o l 12.0 g = 0.5 m o l .
Determine the moles of HCl reacted: n H Cl = 2 × 0.5 m o l = 1 m o l .
Calculate the mass of HCl reacted: ma s s H Cl = 1 m o l × 36.5 g / m o l = 36.5 g .
Calculate the mass of M g C l 2 produced: ma s s M g C l 2 = 0.5 m o l × 95 g / m o l = 47.5 g .
The mass of HCl reacted is 36.5 g and the mass of M g C l 2 produced is 47.5 g .
Explanation
Problem Introduction Let's break down this problem step by step! We're given a chemical reaction where magnesium ( M g ) reacts with hydrochloric acid ( H Cl ) to produce magnesium chloride ( M g C l 2 ) and hydrogen gas ( H 2 ). Our goal is to find out how much H Cl is needed to react with 12.0 g of M g , and how much M g C l 2 is produced.
Calculating Moles of Magnesium First, we need to find out how many moles of magnesium we have. We know that we have 12.0 g of M g , and the molar mass of M g is 24 g/mol. To find the number of moles, we use the formula: n = M o l a r M a ss ma ss So, the number of moles of M g is: n M g = 24 g / m o l 12.0 g = 0.5 m o l
Calculating Moles of Hydrochloric Acid Now that we know the number of moles of M g , we can use the balanced chemical equation to find out how many moles of H Cl are needed. The balanced equation is: M g ( s ) + 2 H Cl ( a q ) ⟶ M g C l 2 ( a q ) + H 2 ( g ) From the equation, we see that 1 mole of M g reacts with 2 moles of H Cl . So, the number of moles of H Cl needed is: n H Cl = 2 × n M g = 2 × 0.5 m o l = 1 m o l
Calculating Mass of Hydrochloric Acid Next, we need to find the mass of H Cl that corresponds to 1 mole. The molar mass of H Cl is approximately 36.5 g/mol. So, the mass of H Cl needed is: ma s s H Cl = n H Cl × M o l a r M a s s H Cl = 1 m o l × 36.5 g / m o l = 36.5 g
Calculating Mass of Magnesium Chloride Now, let's calculate the mass of M g C l 2 produced. From the balanced equation, we see that 1 mole of M g produces 1 mole of M g C l 2 . So, the number of moles of M g C l 2 produced is the same as the number of moles of M g reacted, which is 0.5 mol. The molar mass of M g C l 2 is approximately 95 g/mol. So, the mass of M g C l 2 produced is: ma s s M g C l 2 = n M g C l 2 × M o l a r M a s s M g C l 2 = 0.5 m o l × 95 g / m o l = 47.5 g
Final Answer Therefore, when 12.0 g of M g reacts with dilute hydrochloric acid, 36.5 g of H Cl is reacted and 47.5 g of M g C l 2 is produced.
Examples
This type of calculation is crucial in various fields, such as chemical engineering, environmental science, and pharmaceuticals. For instance, in wastewater treatment, we might need to determine the amount of acid required to neutralize a certain amount of alkaline waste. Similarly, in the production of medications, precise calculations are necessary to ensure the correct proportions of reactants, leading to the desired product. Understanding stoichiometry and molar mass calculations allows us to efficiently plan and execute chemical processes, optimizing resource usage and minimizing waste.
When 12.0 g of magnesium reacts with dilute hydrochloric acid, 36.5 g of hydrochloric acid is consumed, and 47.5 g of magnesium chloride is produced. This is calculated using the molar masses and the stoichiometry of the chemical reaction. The key steps include calculating the moles of magnesium, determining the required moles of hydrochloric acid, and finding the masses of both hydrochloric acid and magnesium chloride formed.
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