im given the refractive index values of two - isobutyl bromide (1.3785) and isobutyl chloride (2.4368).
the solution's refractive index is 1.3931.
determine the molar composition (%).
im not sure how to get the concentrations of Br and Cl.
i have this so far-
100 * 1.3931= [Br] * 1.4368 + 1.3785 * [Cl]
thanks!
Yes, and the second equation is that the sum of both percents is 100. So replace the percent Cl with (100-Br), and solve for Br percent.
Am I missing something here?
I get a negative number. Isn't it supposed to be
100*1.3931 = 1.3785*Br + 1.4368*Cl
To determine the molar composition of the solution, you need to set up a system of equations using the given refractive index values and the unknown concentrations of Br (isobutyl bromide) and Cl (isobutyl chloride).
Let's assume the molar concentration of Br is [Br] and the molar concentration of Cl is [Cl]. Here's how you can set up the equations:
1. From the given refractive indices:
1.3931 = [Br] * 1.4368 + [Cl] * 1.3785 --- (equation 1)
2. Since this is a solution, the molar concentrations of Br and Cl should add up to 100%:
[Br] + [Cl] = 1 --- (equation 2)
Now, you have two equations with two unknowns ([Br] and [Cl]). To solve this system, you can use substitution or elimination.
Let's solve it using substitution:
1. Rearrange equation 2 to express [Cl] in terms of [Br]:
[Cl] = 1 - [Br]
2. Substitute this expression for [Cl] in equation 1:
1.3931 = [Br] * 1.4368 + (1 - [Br]) * 1.3785
3. Simplify and solve for [Br]:
1.3931 = 1.4368[Br] + 1.3785 - 1.3785[Br]
0.0146[Br] = 0.0146
[Br] = 1
4. Substitute the value of [Br] back into equation 2 to find [Cl]:
[Cl] = 1 - [Br]
[Cl] = 1 - 1
[Cl] = 0
Now you have the molar concentrations [Br] = 1 and [Cl] = 0. Since [Br] represents the molar composition, you can say that the solution is 100% isobutyl bromide (Br) and 0% isobutyl chloride (Cl).
Therefore, the molar composition of the solution is 100% isobutyl bromide and 0% isobutyl chloride.