Answer to Question #146176 in General Chemistry for Brittany Shuler

Question

What volume (in mL) of a 1.000 M solution of NaOH is required to make 56.9 mL of 0.25 M NaOH?

Answer 1

Q146176

What volume (in mL) of a 1.000 M solution of NaOH is required to make 56.9 mL of 0.25 M NaOH?

Solution:

We can solve this problem by two methods.

Method 1: By using the dilution formula, M _i V_i = M_f V_f ;

Method 2: By using the formula of molarity.

Method 1: By using the dilution formula, M _i V_i = M_f V_f ;

We have to prepare 56.9mL of 0.25M NaOH solution from 1.000M NaOH solution.

We have to find the volume of 1.000M NaOH solution ( stock solution) required to prepare

56.9mL of 0.25M NaOH solution.

So, final concentration , M_f = 0.25M ,

Final volume, V_f = 56.9mL

Initial concentration, M_i = 1.000M

Initial volume, V_i = unknown.

Substitute all this information in the dilution formula we have

1.000M * V_i = 0.25M * 56.9mL ;

divide both the side by 1.000M , we have

1.000M * V_i / 1.000M= 0.25M * 56.9mL/ 1.000M ;

V_i = 14.225mL ;

In question, the quantity with the least number of significant figures is 0.25M. It is in 2 significant figure, so our final answer must also be in 2 significant figures.

Hence we require 14mL of 1.000M for the preparation of 56.9 mL of 0.25 M NaOH

Method 2: By using the formula of molarity.

Step 1: Find the moles of NaOH present in 56.9 mL of 0.25 M NaOH solution.

Molarity = moles of solute/volume of solution in ‘ L ’

We have to prepare 56.9 mL of 0.25 M NaOH;

Convert 56.9mL to ‘L’ using the conversion factor, 1L = 1000mL.

So the volume in ‘L’ is = 56.9 mL * 1 L/ 1000mL = 0.0569 L

Substitute 0.25M and 0.0569L in the formula of molarity we have

0.25M = moles of NaOH/ 0.0569 L ;

multiply both the side by 0.0569L, we have

0.25mol/L * 0.0569 L = moles of NaOH/ 0.0569 L * 0.0569 L ; ( M = mol/ L)

0.01423 mol = moles of NaOH ;

Step 2 : From 0.01423 mol NaOH and concentration 1.000M NaOH, find the volume of 1.000M NaOH solution ( stock solution )

plug 0.01423 mol and 1.000M in the molarity formula and find the volume of stock solution of NaOH

Molarity = moles of solute / volume of solution in ‘ L ’

1.000M = 0.01423 mol / volume of stock NaOH solution

1.000mol/L = 0.01423 mol /volume of stock NaOH solution

Arranging this equation we have

volume of stock NaOH solution = 0.01423 mol / 1.000mol/L = 0.01423 L ;

Convert 0.01423L to mL using 1L = 1000mL;

volume of stock NaOH solution in mL = 0.01423 L * 1000 mL/1L = 14.23 mL ;

which in the correct significant figure is 14mL.

Hence the volume of 1.000M NaOH solution required is 14 mL