The absorbance of $2$ $2$ x $10^{- 4}$ $10^-4$ $M$ $M$ solution was found to be $0.123$ $0.123$ when placed in a cell of $1$ $1$ $c m$ $cm$ length. Calculate the transmittance, percent transmittance and molar absorptivity of a cell of length $2$ $2$ $c m$ $cm$ ?

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The absorbance of $2$ $2$ x $10^{- 4}$ $10^-4$ $M$ $M$ solution was found to be $0.123$ $0.123$ when placed in a cell of $1$ $1$ $c m$ $cm$ length. Calculate the transmittance, percent transmittance and molar absorptivity of a cell of length $2$ $2$ $c m$ $cm$ ?

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Answer 1 · 2016-02-12T16:34:12

$T = 0.568$ $T=0.568$
$% T = 56.8 %$ $%T=56.8%$
$ε = 615 M^{- 1} \cdot c m^{- 1}$ $epsilon=615M^(-1)*cm^(-1)$

Explanation:

$C = 2 \times 10^{- 4} M$ $C=2xx10^(-4)M$
$A = 0.123$ $A=0.123$
$l = 2 c m$ $l=2cm$
$? T$ $?T$ , $? % T$ $?%T$ , $? ε$ $?epsilon$

The relationship between transmittance $T$ $T$ and absorbance is:

$A = - log T \Rightarrow T = 10^{- A}$ $A=-logT=>T=10^(-A)$

Since the length of the cell was increased to $l = 2 c m$ $l=2cm$ , the absorbance will double and therefore, $A_{2} = 2 \times 0.123 = 0.246$ $A_2=2xx0.123=0.246$

$\Rightarrow T = 10^{- 0.246} = 0.568$ $=>T=10^(-0.246)=0.568$

Therefore, $% T = 100 \times T = 100 \times 0.568 = 56.8 %$ $%T=100xxT=100xx0.568=56.8%$

In order to solve for the molar absorptivity $ε$ $epsilon$ , we will use the Beer-Lambert law:

$A = ε \times l \times C \Rightarrow ε = \frac{A}{l \times C}$ $A=epsilonxxlxxC=>epsilon=A/(lxxC)$

$ε = \frac{0.123}{1 c m \times 2 \times 10^{- 4} M} = 615 M^{- 1} \cdot c m^{- 1}$ $epsilon=(0.123)/(1cmxx2xx10^(-4)M)=615M^(-1)*cm^(-1)$

Here is a video that explains Beer-Lambert law and it use experimentally:
AP Chemistry Investigation #1: Beer-Lambert Law.

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The absorbance of $2$ $2$ x $10^{- 4}$ $10^-4$ $M$ $M$ solution was found to be $0.123$ $0.123$ when placed in a cell of $1$ $1$ $c m$ $cm$ length. Calculate the transmittance, percent transmittance and molar absorptivity of a cell of length $2$ $2$ $c m$ $cm$ ?

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Explanation:

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The absorbance of $2$ $2$ x $10^{- 4}$ $10^-4$ $M$ $M$ solution was found to be $0.123$ $0.123$ when placed in a cell of $1$ $1$ $c m$ $cm$ length. Calculate the transmittance, percent transmittance and molar absorptivity of a cell of length $2$ $2$ $c m$ $cm$ ?