Question

This question has multiple correct options.
a.) 166 g of KI per litre solution.
b.) 33.0 g (NH$_4$)$_2$SO$_4$ in 200 mL solution.
c.) 25.0 g CuSO$_4$.5H$_2$O in 100 mL solution.
d.) 27.0 mg Al$^{3+}$ per mL solution.

Answer 1

Hint: In this question we have to calculate the molar concentration. We are given with the used weight of molecules to form a solution. We will calculate the number of moles, or in terms of mass, molarity can be calculated.


Complete step by step solution:
First, we will define the molarity; it is related to the moles of solute, and volume of solution.
We can say that the molarity is the ratio of moles of solute to that of the volume of solution in the litres.
First, we will calculate the molecular weight of molecules given in the options.
 Molecular weight of KI = 40 + 126 = 166 g/mol
 Molecular weight of (NH$_4$)$_2$SO$_4$ = 132 g/mol
 Molecular weight of CuSO$_4$.5H$_2$O = 250 g/mol
 Molecular weight of Al$^{3+}$ = 27g/mol
Let us write the formula of molarity, or molar concentration
Molarity = n/ V
Here, n represents the number of moles, and V represents the volume of solution.
So, let us look at the given options.
The first is 166 g of KI per litre solution
Molarity = $\dfrac{166 \times 1000}{166 \times 1000}$, Here n = 166/166
For KI, the molecular weight is 166 g/mol, and given weight is also 166 g/mol
Molarity = 1.0 M
The second is 33.0 g (NH$_4$)$_2$SO$_4$ in 200 mL solution
Molarity = $\dfrac{33 \times 1000}{132 \times 200}$, Here n = 33/132
The molecular weight is 132 g/mol, and given weight is 33 g/mol.
Molarity = 1.25 M
The third is 25.0 g CuSO$_4$.5H$_2$O in 100 mL solution.
Molarity = $\dfrac{25 \times 1000}{250 \times 100}$, Here n = 25/250
The molecular weight is 250 g/mol, and given weight is 25 g/mol.
Molarity = 1.0 M
The fourth option is 27.0 mg Al$^{3+}$ per mL solution.
Molarity = $\dfrac{27 \times 10^{-3} \times 1000}{27 \times 1}$, Here n = 27 $\times$ 10$^{-3}$ /27
The molecular weight is 27 g/mol, and given weight is 27 $\times$ 10$^{-3}$ g/mol.
Molarity = 1.0 M
So, in the last we can say that the first, third, and the fourth option has the same molar concentration.

Hence, the correct options are (A), (C), and (D).

Note: Don’t get confused while the calculation of molar concentration. Move step by step as shown. The volume in some options is given in mL so we have divided it by 1000. In the fourth option, we have the value of given weight in mg so, we divided it by 1000 while calculating the number of moles.