Question

What is the molarity if a 500mL solution contains 20g of $\text{CaB}{{\text{r}}_{\text{2}}}$?

Answer 1

The atomic mass of Ca is $\text{40g/mol}$ and Br is $\text{80g/mol}$
The molarity of a solution can be calculated using the formulae,
$\text{Molarity=}\dfrac{\text{No}\text{.}\,\text{of}\,\text{moles}}{\text{Volume}}\text{ }\\!\\!\times\\!\\!\text{ 1000}$

Complete step by step answer:
- So in the question it is asked that what will be the molarity of the solution with a volume of 500mL and has 20g of $\text{CaB}{{\text{r}}_{\text{2}}}$ in them. Before going into the solution part we should know about the solution and the components in them.
- We can define a solution as the homogeneous mixture of two or more substances and we generally refer to solutions as those mixtures which are in liquid state but mixtures with other physical states are also called as the solution.
- In a solution there are mainly two components present and the components are solute and a solvent.
- Solute is the substance which gets dissolved uniformly in a given medium and we commonly refer to the solid substances as the solutes.
- The solvent is the medium in which the solute is dissolved to make up the solution.
Now we know the components in a solution, then the question that arises in our mind is about how to represent the concentration of the solution by relating the solute and solvent measurement.
One of the concentration parameters used is the molarity.
- Molarity is the concentration parameter used for the solution and is defined calculated by dividing the number of moles with the volume of solution in liters.
- Now let’s solve the equation, for that, let’s write the information given in the question.
It is given that the volume of solution is 500mL
Since the volume is given in milliliter the equation for molarity will be multiplied with 1000 and the equation for molarity is,
$\text{Molarity=}\dfrac{\text{No}\text{.}\,\text{of}\,\text{moles}}{\text{Volume}}\text{ }\\!\\!\times\\!\\!\text{ 1000}$
- To find the molarity we should know the number of moles of the solute. Hence lets first calculate the number of moles of solute.
The equation to calculate the number of moles of solute is, $\text{No}\text{.}\,\,\text{of}\,\text{moles}\,\text{of}\,\text{solute=}\dfrac{\text{Given}\,\text{mass}\,\text{of}\,\text{solute}}{\text{Molecular}\,\text{mass}\,\text{of}\,\text{solute}}$
The $\text{CaB}{{\text{r}}_{\text{2}}}$ is the solute here and the given weight of $\text{CaB}{{\text{r}}_{\text{2}}}$ is 20 g.
- Now we should know the value of molecular mass of $\text{CaB}{{\text{r}}_{\text{2}}}$
The atomic mass of Ca is 40 and that of Br is 80.
- Hence the molecular mass is the total sum of the atomic mass of individual atoms present in the compound.
$\text{Molecular}\,\text{mass}\,\text{of}\,\text{CaB}{{\text{r}}_{\text{2}}}\text{=40+2}\left( \text{80} \right)\text{=200 g}$
- Now substitute these values in the equation for number of moles,
$\text{No}\text{.}\,\,\text{of}\,\text{moles}\,\text{of}\,\text{solute=}\dfrac{\text{20}}{\text{200}}\text{=0}\text{.1moles}$
- Substitute the values in the equation for molarity.
$\text{Molarity=}\dfrac{\text{No}\text{.}\,\text{of}\,\text{moles}}{\text{Volume}}\text{ }\\!\\!\times\\!\\!\text{ 1000}$
$\text{Molarity=}\dfrac{\text{0}\text{.1}}{\text{500}}\text{ }\\!\\!\times\\!\\!\text{ 1000=0}\text{.2M}$
Hence we got the value of molarity of the solution which is 0.2 M

Note: We can also convert the volume of the solution into liter first and then we could substitute the value obtained directly into the equation.
If we are provided with the mass of the solvent then we could find the molality of the solution.
$\text{Molarity=}\dfrac{\text{No}\text{.}\,\text{of}\,\text{moles}}{\text{Mass}\,\text{of}\,\text{solvent}\,\text{in}\,\text{Kg}}$