The diffusion current for a standard is 1 x 10^-4M solution of hydroquinone is 17.5 microamperes. An unknown solution of hydroquinone, when diluted hundred folds and polarographed under same conditions yielded a current of 30.5 microamperes. Calculate the concentration of hydroquinone in the unknown sample.

To calculate the concentration of hydroquinone in the unknown sample, we can use the equation:

C₁V₁ = C₂V₂

Where:
C₁ is the concentration of the standard solution (1 x 10^-4 M),
V₁ is the volume of the standard solution (unknown),
C₂ is the concentration of the unknown solution (unknown),
V₂ is the volume of the unknown solution (100 times the volume of the standard solution).

We have the diffusion currents for both the standard and the unknown solutions. The diffusion current is directly proportional to the concentration of the analyte. So, we can use the following proportion to relate the diffusion currents:

I₁/I₂ = C₁/C₂

Where:
I₁ is the diffusion current for the standard solution (17.5 microamperes),
I₂ is the diffusion current for the unknown solution (30.5 microamperes).

Now, let's substitute the given values into the equations and solve for C₂ (the concentration of the unknown solution):

C₁V₁ = C₂V₂
C₁ = 1 x 10^-4 M
V₁ = unknown (we'll solve for this)
C₂ = unknown (we'll solve for this)
V₂ = 100 x V₁

I₁/I₂ = C₁/C₂
I₁ = 17.5 microamperes
I₂ = 30.5 microamperes

First, let's solve for V₂:

V₂ = 100 x V₁

Next, let's solve for C₂:

I₁/I₂ = C₁/C₂

C₂ = (C₁ x I₂) / I₁
C₂ = (1 x 10^-4 M x 30.5 microamperes) / 17.5 microamperes

Now, let's solve for V₁ using the equation C₁V₁ = C₂V₂:

C₁V₁ = C₂V₂
(1 x 10^-4 M) x V₁ = C₂ x (100 x V₁)

Now, substitute the value of V₂ and solve for V₁:

(1 x 10^-4 M) x V₁ = [(1 x 10^-4 M x 30.5 microamperes) / 17.5 microamperes] x (100 x V₁)

Now, cancel out the V₁ terms and solve for the concentration C₂:

C₂ = (1 x 10^-4 M x 30.5 microamperes) / (17.5 microamperes)

After calculating the value of C₂, you will have the concentration of hydroquinone in the unknown sample.