Question

How many moles are there in 4.75 g of magnesium chloride?

Answer 1

For the determination of the number of moles of a substance we will carry out the division operation between the weight of the sample given and the molecular mass of the sample given.
The equation by which we calculate the number of moles of the substance is, $\text{Number}\,\text{of}\,\text{moles}\,\text{of}\,\text{sample}\,=\,\dfrac{\text{Weight of the given sample}}{\text{Molar mass of the sample}}$

Complete step by step answer:
So in the question, it is asked to find the number of moles of magnesium chloride for the given weight of magnesium chloride.
Before going into the solution part of the question, let’s first discuss the concept of mole.
Mole is the quantity parameter which is used to measure large amounts of units like ions, atoms, molecules etc in the substance. And one mole of the substance consists of $6.022\times {{10}^{23}}$ particles ( say atoms, molecules etc) in them. And this constant value $6.022\times {{10}^{23}}$, is called the Avogadro number of Avogadro constant.
Now we have to find out how many moles of substance is present in the given weight of magnesium chloride. For that we have to know the formulae of the substance so that we can calculate the molar mass of the substance to substitute in the equations.
Now we have to know in which composition the atoms in magnesium chloride is combining to form the compound and it can be calculated from the formulae.
The formulae of magnesium chloride is $\text{MgC}{{\text{l}}_{\text{2}}}$.
So from the equation we know that the one magnesium atom needs two Cl atoms for the formation of $\text{MgC}{{\text{l}}_{\text{2}}}$
And to find the molar mass of the compound we have simply add the atomic mass of the elements.Since two Cl is present we have to add the atomic mass of Cl twice.
Atomic mass of Mg is $24.305g/mol$ and Cl is $35.4g/mol$
Hence, $\text{Molar}\,\text{mass of MgC}{{\text{l}}_{\text{2}}}\,=\,24.305\,+\,2\left( 35.453 \right)\,=\,\text{95}\text{.211g/mol}$
So now we know the molar mass of the $\text{MgC}{{\text{l}}_{\text{2}}}$ and we know the weight of is $\text{MgC}{{\text{l}}_{\text{2}}}$taken.
Let's write the equation for calculating the number of moles of $\text{MgC}{{\text{l}}_{\text{2}}}$.$\text{Molar}\,\text{mass of MgC}{{\text{l}}_{\text{2}}}\,=\,\text{95}\text{.211g/mol}$
$\text{Number}\,\text{of}\,\text{moles}\,\text{of}\,\text{MgC}{{\text{l}}_{\text{2}}}\,\text{=}\,\dfrac{\text{Weight}\,\text{of}\,\text{MgC}{{\text{l}}_{\text{2}}}}{\text{Molar}\,\text{mass}\,\text{of}\,\text{MgC}{{\text{l}}_{\text{2}}}}$
$\text{Molar}\,\text{mass of MgC}{{\text{l}}_{\text{2}}}\,=\,\text{95}\text{.211g/mol}$
$\text{Given}\,\text{weight}\,\text{of}\,\text{MgC}{{\text{l}}_{\text{2}}}\,\text{=}\,\text{4}\text{.75g}$
Substitute the values in the equation to get the number of moles of magnesium chloride.$\text{Number}\,\text{of}\,\text{moles}\,\text{of}\,\text{MgC}{{\text{l}}_{\text{2}}}\,\text{=}\,\dfrac{4.75g}{95.211{g}/{mol}\;}=0.04988mol$
Hence we got the final as , ie the number of moles of $\text{MgC}{{\text{l}}_{\text{2}}}$in the given weight is 0.04988 mol

Note: We should know the atomic mass of the elements, so that we can calculate the molar mass of the compound given and we should know how to write the chemical formulae of the compound. Since we have to know the ratio of the atoms that have combined to give the chemical compound for the molar mass calculation.
- We could rearrange the equation above given to find the weight of the sample, if molar mass and weight of the sample is known.