Question

Grams of solute needed to make 475 ml of $ 5\cdot 62\times {{10}^{-2}} $ m potassium sulfate-
(A) $ 4\cdot 65 $ g
(B) $ 46\cdot 5 $ g
(C) $ 0\cdot 465 $ g
(D) $ 9\cdot 30 $ g

Answer 1

Hint: The concentration of potassium sulphate is given along with volume of the solution. So, from here we can find the no. of moles and then using the molar mass of potassium sulfate we will find the required mass of solute. The no. of moles is given by the given mass divided by the molar mass of the compound.

Formula Used: concentration $ = $ no. of moles/volume in liters

Complete Step By Step Solution
Finding the no. of moles we get,
Concentration $ = $ no. of moles/volume in liters
   $ 5\cdot 62\times {{10}^{-2}}=\dfrac{\text{no}\text{.}\,\text{of}\,\text{moles}}{\text{475ml}} $
 $ 5\cdot 62\times {{10}^{-2}}=\dfrac{\text{no}\text{.}\,\text{of}\,\text{moles}\times 1000}{475\text{l}} $
 $ \text{No}\text{. of mole}=\dfrac{5\cdot 62\times {{10}^{-2}}\times 475}{1000} $
 $ \begin{align}
  & =2669\cdot 5\times 10 \\
 & \,=0\cdot 0267 \\
\end{align} $
So, no. of moles $ =0\cdot 0267 $
Molar mass of potassium sulfate:
 $ \begin{align}
  & ({{\text{K}}_{2}}\text{S}{{\text{O}}_{4}})=39\times 2+32+16\times 4 \\
 & \Rightarrow 78+32+64 \\
 & \Rightarrow 174g/mol \\
\end{align} $
Using no. of moles = required mass/molar mass
 $ 0\cdot 0267=\dfrac{\text{required}\,\text{mass}}{\text{174}} $
 $ \text{required mass}=0\cdot 0267\times 174 $
 $ \Rightarrow 4\cdot 65g $
So the correct choice is (A).

Additional Information
Mole is the unit to measure the amount of substance which describes that Avogadro number of atoms or molecules or ions are present in one mole of a substance. Avogadro number equals to the value $ 6\cdot 023\times {{10}^{23}} $ . The molar mass for a compound can be easily found by adding the molar masses or atomic masses of its constituent elements. The atomic mass or mass number of an element is the sum of no. of protons and no. of neutrons contained in them. It is represented by A. One can determine the atomic no. of an element if its mass no. and no. of neutrons are known because atomic no. is the no. of protons for an element. It is represented by Z.

Note
The volume in the above used formula should always be written in liters. The conversion of $ 1 $ liter into milli-liters is $ 1 $ liter $ =1000 $ ml. One should know the method to find out no. of moles and the respective molar masses for compounds. The knowledge and understanding of periodic tables is must to find out the mass no. for various elements. The molar mass is given in grams per mole so the units of required mass will also be in grams.