A solution containing 3.47 mM X (analyte) and 1.65 mM S (internal standard) gave peak areas of 3321 and 9762, respectively, in a chromatographic analysis. Then 1.00 ml of 8.47 mM S was added to 5.00 ml of unknown X, and the mixture was diluted to 10.0 ml. This solution gave peak areas of 5428 and 4431 for X and S, respectively. Answer the following questions and enter your results with numerical values only.

A. Calculate the response factor for the analyte. (keep four significant figures)

B. Find the concentration (mM) of X in the 10.0 ml of mixed solution.

C. Find the concentration (mM) of X in the original unknown.

### Step 1 of 2

Given data: A solution containing 3.47 mM X (analyte) and 1.65 mM S (internal standard) gave peak areas of 3321 and 9762, respectively, in a chromatographic analysis. Then 1.00 ml of 8.47 mM S was added to 5.00 ml of unknown X, and the mixture was diluted to 10.0 ml. This solution gave peak areas of 5428 and 4431 for X and S, respectively.

Find: A. Calculate the response factor for the analyte.

- Find the concentration (mM) of X in the 10.0 ml of mixed solution.
- Find the concentration (mM) of X in the original unknown.

**Explanation:**

To calculate the response factor for the analyte (X), we can use the peak areas and concentrations of X and the internal standard (S). The response factor is defined as the ratio of the peak area of the analyte to the peak area of the internal standard.

### Step 2 of 2

Let’s go through each question step by step:

**Calculate the response factor for the analyte:**

The response factor (RF) is the ratio of the analyte peak area to the internal standard peak area.

The formula is:

RF=Peak area of analytePeak area of Internal standardRF(X)=97,623,321RF(X)=0.3402

**Find the concentration (mM) of X in the 10.0 ml of mixed solution:**

The concentration of X in the mixed solution can be calculated using the formula:

Concentration of X=RF × Concentration of Internal standard × Peak area of analytePeak area of Internal standardConcentration of X=0.3402× 1.65× 5,4284,431Concentration of X=0.4171 mM

**Find the concentration (mM) of X in the original unknown:**

The concentration of X in the original unknown can be calculated using the formula:

Concentration of X=Concentration of X In mixed solution × Volume of mixed solutionVolume of Orignal unknownConcentration of X=0.417 × 105Concentration of X=0.8342 mM

**Explanation:**

Hence, we have used the peak areas and concentrations of X and the internal standard (S).

##### Final solution

So, the answers are:

- The response factor for the analyte is approximately 0.3402.
- The concentration of X in the 10.0 ml mixed solution is approximately 0.4171mM.
- The concentration of X in the original unknown is approximately 0.8342mM.