Substance X has a molar extinction coefficient (E) of 4725 l.mol-1 cm-1. How many micromoles of X are needed to produce an absorbance of 1.0 in a 1 ml cuvette?
To determine the number of micromoles of Substance X needed to produce an absorbance of 1.0 in a 1 ml cuvette, we can use the Beer-Lambert Law, which describes the relationship between absorbance, molar extinction coefficient, concentration, and path length.
The Beer-Lambert Law is expressed as follows:
A = εcl
Where:
A is the absorbance,
ε (epsilon) is the molar extinction coefficient,
c is the concentration in moles per liter (Molar concentration),
l is the path length in centimeters.
In this case, we have the absorbance (A) as 1.0, the path length (l) as 1 cm, and the molar extinction coefficient (ε) as 4725 L.mol-1.cm-1.
We need to calculate the concentration (c) in moles per liter to solve for the number of micromoles of Substance X.
Rearranging the Beer-Lambert Law equation, we get:
c = A / (εl)
Substituting the given values, we have:
c = 1.0 / (4725 L.mol-1.cm-1)(1 cm)
To convert L to mL and cm to mL, we can use the conversion:
1 L = 1000 mL
1 cm = 0.1 mL
c = 1.0 / (4725 mL.mol-1.(0.1 mL))
Simplifying the above expression, we get:
c = 1.0 / (4725 * 0.1) mol mL-1
c = 1.0 / 472.5 mol mL-1
Next, we need to convert milliliters (mL) to liters (L) since the concentration units are in moles per liter (Molar concentration):
c = 1.0 / 0.4725 mol L-1
Now, to calculate the number of micromoles, we will use the given volume of 1 mL:
1 mL = 0.001 L
c = 1.0 / 0.4725 mol (0.001 L)
c = 1.0 / 0.0004725 mol
c = 2116.98 mol
Finally, we convert moles to micromoles:
1 mole = 10^6 micromoles
Therefore, the number of micromoles of Substance X needed to produce an absorbance of 1.0 in a 1 mL cuvette is approximately 2116.98 micromoles.