Answer :
To find the normality of a solution of phosphoric acid (
�
3
�
�
4
H
3
PO
4
) that contains 50.0 g per liter of solution, we first need to determine the molarity of the solution. Then, we can calculate the normality using the following relationship:
Normality (N)
=
Molarity (M)
×
Equivalent factor
Normality (N)=Molarity (M)×Equivalent factor
The equivalent factor for phosphoric acid (
�
3
�
�
4
H
3
PO
4
) is 3 because each molecule of phosphoric acid can donate three protons (H⁺ ions) in a reaction.
Step 1: Calculate the molarity of the solution
The molar mass of phosphoric acid (
�
3
�
�
4
H
3
PO
4
) can be calculated as follows:
Molar mass of
�
3
�
�
4
=
(
3
×
molar mass of H
)
+
molar mass of P
+
(
4
×
molar mass of O
)
Molar mass of H
3
PO
4
=(3×molar mass of H)+molar mass of P+(4×molar mass of O)
=
(
3
×
1.008
g/mol
)
+
30.974
g/mol
+
(
4
×
16.00
g/mol
)
=(3×1.008g/mol)+30.974g/mol+(4×16.00g/mol)
=
97.998
g/mol
=97.998g/mol
Now, we can use the definition of molarity to calculate the molarity (
�
M):
�
=
moles of solute
volume of solution in liters
M=
volume of solution in liters
moles of solute
Given that the solution contains 50.0 g of phosphoric acid per liter, we can calculate the moles of phosphoric acid per liter using its molar mass:
moles of
�
3
�
�
4
=
mass of
�
3
�
�
4
molar mass of
�
3
�
�
4
moles of H
3
PO
4
=
molar mass of H
3
PO
4
mass of H
3
PO
4
=
50.0
g
97.998
g/mol
=
97.998g/mol
50.0g
≈
0.510
mol/L
≈0.510mol/L
Step 2: Calculate the normality
Now that we have the molarity, we can use the equivalent factor to find the normality:
Normality (N)
=
Molarity (M)
×
Equivalent factor
Normality (N)=Molarity (M)×Equivalent factor
=
0.510
mol/L
×
3
=0.510mol/L×3
=
1.53
N
=1.53N
So, the normality of the solution of phosphoric acid that contains 50.0 g per liter of solution is approximately
1.53
N
1.53N.