Question

Calculate the final concentration of each of the following:

a. 1.0Lof a 4.0M {HNO}3 solution is added to the water so that the final volume is 8.0L.

b. Water is added to 0.25 L of a 6.0 NaF solution to make 2.0L of a diluted NaF solution.

c. A 50.0mL sample of an 8.0 % KBr solution is diluted with water so that the final volume is 200.0mL.

d. A 5.0mL sample of a 50.0 % acetic acid $\left({\mathrm{HC}}_2{\mathrm{H}}_3{\mathrm{O}}_2\right)$solution is added to water to give a final volume of 25mL..

Short answer

a. the final concentration is$0.5M$

b. the final concentration is$0.75M$

c. the final concentration is$2\mathrm{\%}(\mathrm{M}/\mathrm{V})$

d. the final concentration is$10\%(M/V)$

Step-by-step solution

Part (a) Step 1: Given Information

$1$L of a $4$M $HN{O}_3$ solution is added to the water so that the final volume is $8$L.

Part (a) Step 2: Explanation

Using the concentration formula,

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

role="math" localid="1653929520012" $C_1=4\mathrm{M},V_1=1\mathrm{L},{\mathrm{V}}_2=8\mathrm{L}$

The final concentration is,

$c_2=\frac{c_1{v}_1}{v_2}=4\mathrm{M}\times \frac{1L}{8L}=0.5\text{M}$

Part (b) Step 1: Given Information

Water is added to $0.25$L of a $6$ NaF solution to make $2$L of a diluted NaF solution.

Part (b) Step 2: Explanation

Using the concentration formula,

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

role="math" localid="1653929779239" $C_1=6M,V_1=0.25L,V_2=2L$

The final concentration is,

$c_2=\frac{c_1{v}_1}{v_2}=6\mathrm{M}\times \frac{0.25\mathrm{L}}{2\mathrm{L}}=0.75\mathrm{M}$

Part (c) Step 1: Given Information

A $50$mL sample of an $8$% KBr solution is diluted with water so that the final volume is $200$mL.

Part (c) Step 2: Explanation

Given,

$C_1=8\mathrm{\%}(M/V),V_1=50\mathrm{mL},V_2=200\mathrm{mL}$

Using the dilution factor = $\frac{V_2}{V_1}$

The dilution factor =$\frac{200}{50}=4$

Now, The concentration is

$\mathrm{\%}M/V=\frac{1}{4}\times 8\mathrm{\%}=2\%$

Part (d) Step 1: Given Information

A $5$mL sample of a $50$% acetic acid solution is added to water to give a final volume of $25$mL.

Part (d) Step 2: Explanation

Given,$C_1=50\mathrm{\%}(M/V),V_1=5\mathrm{mL},V_2=25\mathrm{mL}$

Using the dilution factor = $\frac{V_2}{V_1}$

the dilution factor = role="math" localid="1653930566200" $\frac{25}{5}=5$

Now, The concentration is

$\mathrm{\%}M/V=\frac{1}{5}\times 50\mathrm{\%}=10\%$