33. 15 g of magnesium ( Mg ) was reacted with 40 g of HCl to form magnesium chloride $$ \left(\mathrm{MgCl}_{2} ight) $$ and hydrogen gas as in the following reaction: $$ \mathrm{Mg}(\mathrm{s})+2 \mathrm{HCl}(\mathrm{aq}) ightarrow \mathrm{MgCl}_{2}(\mathrm{aq})+\mathrm{H}_{2}(\mathrm{~g}) $$ Calculate the mass in gram $$ (\mathrm{g}) $$ of $$ \mathrm{MgCl}_{2} $$ formed $$ \begin{array}{llll} ext { A) } 25.7 & ext { C) } 104.8 & 30.7 & ext { D) } 52.2\end{array} $$

Question

33. 15 g of magnesium ( Mg ) was reacted with 40 g of HCl to form magnesium chloride $$ \left(\mathrm{MgCl}_{2}ight) $$ and hydrogen gas as in the following reaction: $$ \mathrm{Mg}(\mathrm{s})+2 \mathrm{HCl}(\mathrm{aq}) ightarrow \mathrm{MgCl}_{2}(\mathrm{aq})+\mathrm{H}_{2}(\mathrm{~g}) $$ Calculate the mass in gram $$ (\mathrm{g}) $$ of $$ \mathrm{MgCl}_{2} $$ formed $$ \begin{array}{llll}	ext { A) } 25.7 & 	ext { C) } 104.8 & 30.7 & 	ext { D) } 52.2\end{array} $$

UpStudy AI · Accepted Answer

To calculate the mass of magnesium chloride ($$ \mathrm{MgCl}_{2} $$) formed in the reaction, we need to use the stoichiometry of the balanced chemical equation provided.

The balanced chemical equation for the reaction is:
$$ \mathrm{Mg}(\mathrm{s}) + 2 \mathrm{HCl}(\mathrm{aq}) \rightarrow \mathrm{MgCl}_{2}(\mathrm{aq}) + \mathrm{H}_{2}(\mathrm{g}) $$

From the balanced equation, we can see that 1 mole of magnesium ($$ \mathrm{Mg} $$) reacts with 2 moles of hydrochloric acid ($$ \mathrm{HCl} $$) to produce 1 mole of magnesium chloride ($$ \mathrm{MgCl}_{2} $$).

Given:
- Mass of magnesium ($$ \mathrm{Mg} $$) = 15 g
- Mass of hydrochloric acid ($$ \mathrm{HCl} $$) = 40 g

We need to calculate the mass of magnesium chloride ($$ \mathrm{MgCl}_{2} $$) formed.

First, we need to find the number of moles of magnesium ($$ \mathrm{Mg} $$) and hydrochloric acid ($$ \mathrm{HCl} $$) used in the reaction.

The molar mass of magnesium ($$ \mathrm{Mg} $$) is 24.31 g/mol.
The molar mass of hydrochloric acid ($$ \mathrm{HCl} $$) is 36.46 g/mol.

Number of moles of magnesium ($$ \mathrm{Mg} $$):
$$ \text{Moles of Mg} = \frac{\text{Mass of Mg}}{\text{Molar mass of Mg}} $$

Number of moles of hydrochloric acid ($$ \mathrm{HCl} $$):
$$ \text{Moles of HCl} = \frac{\text{Mass of HCl}}{\text{Molar mass of HCl}} $$

Since the stoichiometry of the reaction is 1:2 for magnesium ($$ \mathrm{Mg} $$) to hydrochloric acid ($$ \mathrm{HCl} $$), the limiting reactant will determine the amount of magnesium chloride ($$ \mathrm{MgCl}_{2} $$) formed.

Let's calculate the number of moles of magnesium ($$ \mathrm{Mg} $$) and hydrochloric acid ($$ \mathrm{HCl} $$) used in the reaction.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{15}{24.31}$$
- step1: Convert the expressions:
  $$\frac{15}{\frac{2431}{100}}$$
- step2: Multiply by the reciprocal:
  $$15\times \frac{100}{2431}$$
- step3: Multiply:
  $$\frac{15\times 100}{2431}$$
- step4: Multiply:
  $$\frac{1500}{2431}$$
Calculate or simplify the expression $$ 40/36.46 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{40}{36.46}$$
- step1: Convert the expressions:
  $$\frac{40}{\frac{1823}{50}}$$
- step2: Multiply by the reciprocal:
  $$40\times \frac{50}{1823}$$
- step3: Multiply:
  $$\frac{40\times 50}{1823}$$
- step4: Multiply:
  $$\frac{2000}{1823}$$
The number of moles of magnesium ($$ \mathrm{Mg} $$) used in the reaction is approximately 0.617 moles, and the number of moles of hydrochloric acid ($$ \mathrm{HCl} $$) used in the reaction is approximately 1.097 moles.

Since the stoichiometry of the reaction is 1:2 for magnesium ($$ \mathrm{Mg} $$) to hydrochloric acid ($$ \mathrm{HCl} $$), the limiting reactant is magnesium ($$ \mathrm{Mg} $$) because it is used in a smaller molar ratio.

Now, we can calculate the mass of magnesium chloride ($$ \mathrm{MgCl}_{2} $$) formed using the number of moles of magnesium ($$ \mathrm{Mg} $$) used in the reaction.

The molar mass of magnesium chloride ($$ \mathrm{MgCl}_{2} $$) is 95.21 g/mol.

Mass of magnesium chloride ($$ \mathrm{MgCl}_{2} $$) formed:
$$ \text{Mass of MgCl}_{2} = \text{Moles of Mg} \times \text{Molar mass of MgCl}_{2} $$

Let's calculate the mass of magnesium chloride ($$ \mathrm{MgCl}_{2} $$) formed.
Calculate the value by following steps:
- step0: Calculate:
  $$0.617\times 95.21$$
- step1: Multiply the numbers:
  $$58.74457$$
The mass of magnesium chloride ($$ \mathrm{MgCl}_{2} $$) formed in the reaction is approximately 58.74457 grams.

Therefore, the correct answer is not provided in the options given.
The mass of $$ \mathrm{MgCl}_{2} $$ formed is approximately 58.7 grams.

15 g of magnesium ( Mg ) was reacted with 40 g of HCl to form magnesium chloride and
hydrogen gas as in the following reaction:

Calculate the mass in gram of formed

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15 g of magnesium ( Mg ) was reacted with 40 g of HCl to form magnesium chloride and hydrogen gas as in the following reaction: Calculate the mass in gram of formed