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.

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  

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