Question

A 4.00 (±0.01) mL Class A transfer pipet is used to transfer 4.00 mL of a 0.302 (±0.004) M Cu2+ stock solution to a 100.00 (±0.08) Class A volumetric flask. Deionized water is used to bring the flask to volume. Calculate the concentration of the diluted soluion in the volumetric flask and report its absolute uncertainty.

Answer 1

Answer:

concentration of diluted solution = 0.0125 ( ± 0.0002)M

Uncertainty = ± 0.0002  

Explanation:

Given that

Initial volume of Cu2+ = 4.00 (±0.01) mL

Initial molarity 0f Cu2+ = 0.302 (±0.004) M

transferred to  100.00 (±0.08) Class A volumetric flask

first we get amount of water added

100.00 (±0.08) - 4.00 (±0.01)  = 96 ± (0.09)

Now according to  law of dilution

The concentration of Cu2+ after adding water

M1V1 = M2V2

we substitute

0.302 (±0.004) * 4.00 (±0.01) = x * 96 ± (0.09)

Now the multiplication of two digits with uncertainty is

(0.004/0.302) * 100 =  1.32% ;    (0.01/4.00) * 100 = 0.25%

= [0.302 ( ± 1.32% )] * [ 4.00 ± (0.25%)]

= 1.208 ±(1.57%)

1.57/100 * 1.208 = 0.0189

so

= (1.208 ± 0.0189)

now substitute in our previous equation

1.208 ± (0.0189) = x * 96 ± (0.09)

x = 1.208 ± (0.0189) / 96 ± (0.09)

{ 0.09/96 * 100 = 0.094% }

so x = 1.208 ± (1.57%) / 96 ± (0.094% )  

x = 0.0125 ± ( 1.664)

now( 1.664/100 * 0.0125)

= ± 0.000208

Hence

concentration of diluted solution = 0.0125 ( ± 0.0002)M

Uncertainty = ± 0.0002