Q.9.60 - An Introduction to General, Organic, and Biological Chemistry

Question

Determine the initial volume, in millilitres, required to prepare each of the following:

a. 20.0 ml of a 0.250M KNO3 solution using a 6.00M KNO3 solution

b. 25.0ml of a 2.50M ${\mathrm{H}}_2{\mathrm{SO}}_4$ solution using a 12.0M ${\mathrm{H}}_2{\mathrm{SO}}_4$ solution

c. 0.500L of a 1.50M $N{H}_{4}Cl$ solution using a 10.0M $N{H}_{4}Cl$ solution

Step-by-Step Solution

Answer

a. The initial volume, in millilitres is $0.833ml$

b. The initial volume, in millilitres is $5.208$ml

c. The initial volume, in millilitres is $75$ml

Part (a) Step 1: Given Information

$20$ml of a $0.250$M $KN{O}_3$ solution using a $6$M $KN{O}_3$ solution 

Part (a) Step 2: Explanation

Given,

$C_1=6\mathrm{M}, {\mathrm{V}}_2=20.0\mathrm{mL}, {\mathrm{C}}_2=0.250\mathrm{M}\text{, }$

Using the concentration formula,

$C_1{V}_1=C_2{V}_2$

The initial volume, in millilitres is 

$V_1=\frac{C_2{V}_2}{C_1}=20\mathrm{mL}\times \frac{0.25\mathrm{M}}{6\mathrm{M}}=0.833mL$

Part (b) Step 1: Given Information

$25$ml of a $2.5$M ${\mathrm{H}}_2{\mathrm{SO}}_4$ solution using a $12$M ${\mathrm{H}}_2{\mathrm{SO}}_4$ solution 

Part (b) Step 2: Explanation

Given,

$C_1=12M, V_2=25\mathrm{mL}, C_2=2.5\mathrm{M}$

Using the concentration formula,

$C_1{V}_1=C_2{V}_2$

The initial volume, in millilitres is  

${\mathrm{V}}_1=\frac{{\mathrm{C}}_2{\mathrm{V}}_2}{{\mathrm{C}}_1}=25\mathrm{mL}\times \frac{2.5\mathrm{M}}{12\mathrm{M}}=5.208ml$

Part (c) Step 1: Given Information

$0.500$L of a$1.50$M ${\mathrm{NH}}_4\mathrm{Cl}$ solution using a$10$M ${\mathrm{NH}}_4\mathrm{Cl}$ solution

Part (c) Step 2: Explanation

Given,

$C_1=10\mathrm{M}, V_2=0.50\mathrm{L}=500\mathrm{ml}, C_2=1.50\mathrm{M}$

Using the concentration formula, 

$C_1{V}_1=C_2{V}_2$

The initial volume, in millilitres is   

$V_1=\frac{C_2{V}_2}{C_1}=500\mathrm{mL}\times \frac{1.5\mathrm{M}}{10\mathrm{M}}=75ml$