Q.9.111 - An Introduction to General, Organic, and Biological Chemistry

Question

What is the final volume, in millilitres, when 25.0 mL of each of the following solutions is diluted to provide the given concentration? 

a. 10.0% (m/v) HCL solution to give a 2.50% (m/v) HCL solution

b. 5.00M HCL solution to give a 1.00M HCL solution

c. 6.00M HCL solution to give a 0.500M HCL solution

Step-by-Step Solution

Answer

a. the final volume is$100$ml 

b. the final volume is $125$ml

c. the final volume is $300$ml

Part (a) Step 1: Given Information

$10$% (m/v) HCL solution to give a $2.50$% (m/v) HCL solution 

Part (a) Step 2: Explanation

Using the concentration formula,

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

Given,

$C_1=10.0\mathrm{\%}, V_1=25.0\mathrm{mL}, C_2=2.50\mathrm{\%}$

$$\begin{gathered} V_2=\frac{C_1}{C_2}\times V_1=\frac{10.0\mathrm{\%}}{2.5\mathrm{\%}}\times 25.00\mathrm{mL} \\ {V}_2=100mL \end{gathered}$$
 Hence the final volume is $100mL$

Part (b) Step 1: Given Information

$5.00$M HCL solution to give a $1.00$M HCL solution 

Part (b) Step 2: Explanation

Using the concentration formula,

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

Given,

$C_1=6.00\mathrm{M}, V_1=25.0\mathrm{mL}, C_2=0.500\mathrm{M}$

$$\begin{gathered} V_2=\frac{C_1}{C_2}\times V_1=\frac{5.0M}{1.0M}\times 25.00\mathrm{mL} \\ {V}_2=125mL \end{gathered}$$

Hence the final volume is $125mL$

Part (c) Step 1: Given Information

$6.00$M HCL solution to give a $0.500$M HCL solution 

Part (c) Step 2: Explanation

Using the concentration formula,

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

Given,

$C_1=6.00\mathrm{M}, V_1=25.0\mathrm{mL}, C_2=0.500\mathrm{M}.$

$$\begin{gathered} V_2=\frac{C_1}{C_2}\times V_1=\frac{6.0\mathrm{M}}{0.5\mathrm{M}}\times 25.00\mathrm{mL} \\ {V}_2=300mL \end{gathered}$$

Hence the final volume is $300mL$