Question

If given ${\text{4}}{\text{.5}}\,{\text{mL}}$ of ${\text{0}}{\text{.05}}\,{\text{M}}$ magnesium sulfate, how many moles of magnesium sulfate do we have?

Answer 1

The given problem is based on the molarity concept.
Here, we have to use the molarity formula and then use the given values of the molarity and the volume of the solution. Then rearrange the molarity formula for the moles and then calculate them.
Here, the volume of the solution is in milliliters hence, first convert it into liters.

Formula used: The molarity of the substance is calculated as follows:
$\operatorname{Molarity} = \dfrac{{moles\,of\,solute}}{{volume\,of\,solution}}$ …… (i)

Complete step by step answer:
Here, we have to use the molarity formula as given above.
$\operatorname{Molarity} = \dfrac{{moles\,of\,solute}}{{volume\,of\,solution}}$
Here, the solute given is magnesium sulfate ${\text{MgS}}{{\text{O}}_{\text{4}}}$ . Now, rearrange the molarity formula for moles of the solute as follows:
$\Rightarrow \operatorname{Molarity} \,of\,{\text{MgS}}{{\text{O}}_{\text{4}}} = \dfrac{{moles\,of\,{\text{MgS}}{{\text{O}}_{\text{4}}}}}{{volume\,of\,{\text{MgS}}{{\text{O}}_{\text{4}}}solution}}$
$\Rightarrow moles\,of\,{\text{MgS}}{{\text{O}}_{\text{4}}} = \operatorname{Molarity} \,of\,{\text{MgS}}{{\text{O}}_{\text{4}}} \times volume\,of\,{\text{MgS}}{{\text{O}}_{\text{4}}}solution$…… (ii)

Here, the volume of the ${\text{MgS}}{{\text{O}}_{\text{4}}}$ solution should be liters therefore, first convert a volume of ${\text{MgS}}{{\text{O}}_{\text{4}}}$ solution in liters as follows:
$\Rightarrow {\text{1}}\,{\text{L = 1000}}\,{\text{mL}}$
$\Rightarrow {\text{4}}{\text{.5}}\,{\text{mL = }}\dfrac{{{\text{4}}{\text{.5}}\,{\text{mL}}}}{{{\text{1000}}\,{\text{mL}}}}{ \times}\,{\text{L}}$
$\Rightarrow {\text{4}}{\text{.5}}\,{\text{mL}}\,{\text{ = }}\,{\text{4}}{\text{.5}} \times {\text{1}}{{\text{0}}^{ - 3}}\,{\text{L}}$
Thus, the volume of ${\text{MgS}}{{\text{O}}_{\text{4}}}$ solution in liters is
$\Rightarrow {\text{4}}{\text{.5}} \times {\text{1}}{{\text{0}}^{ - 3}}\,{\text{L}}$.

Now, use the rearranged molarity equation for the moles of ${\text{MgS}}{{\text{O}}_{\text{4}}}$ and then calculate the moles of ${\text{MgS}}{{\text{O}}_{\text{4}}}$ the as follows:

Here, substitute ${\text{4}}{\text{.5}} \times {\text{1}}{{\text{0}}^{ - 3}}\,{\text{L}}$ for the volume of the ${\text{MgS}}{{\text{O}}_{\text{4}}}$ solution and ${\text{0}}{\text{.05}}\,{\text{M}}$ for molarity of ${\text{MgS}}{{\text{O}}_{\text{4}}}$ in the rearranged equation (ii).
$\Rightarrow moles\,of\,{\text{MgS}}{{\text{O}}_{\text{4}}} = {\text{0}}{\text{.05}}\,\dfrac{{{\text{mol}}}}{{\text{L}}} \times {\text{4}}{\text{.5}} \times {\text{1}}{{\text{0}}^{ - 3}}\,{\text{L}}$
$\Rightarrow moles\,of\,{\text{MgS}}{{\text{O}}_{\text{4}}} = 2.2{\text{5}} \times {\text{1}}{{\text{0}}^{ - 4}}\,{\text{mol}}$

Thus, the moles of magnesium sulfate are $2.2{\text{5}} \times {\text{1}}{{\text{0}}^{ - 4}}\,{\text{mol}}$.

Note: Molarity is the ratio of the moles of the solute to the volume of the solution in liters. It is one of the concentration units used to represent the concentration of the solution.
It is represented by the letter M. and its unit is mole per liter that is molar. As the molarity is dependent on the volume of the solution hence it is affected by the temperature.
The higher is the molarity higher is the concentration of the solution that is nothing but higher moles of the solute in the solution.