How many LC runs do you need to meet the sample amount requirement for: 1. LC-MS (1ng) 2. NMR (10 mg) 3. X-ray (5g)?

Steps to Solve

1. Calculate Column Volume Used for Runs

The total column volume is calculated as given:

$$ V = \pi \times \left( \frac{4.6 , \text{mm}}{2} \right)^2 \times 250 , \text{mm} = 4154.76 , \text{mm}^3 = 4.15 , \text{mL} $$

Since you can only load samples at half of this volume:

$$ V_{\text{load}} = \frac{4.15 , \text{mL}}{2} = 2.075 , \text{mL} $$

2. Determine Active Sample Weight per Run

Next, calculate the amount of sample weight per run based on the loading capacities of the peaks:

• For Peak 1 (2%): $$ W_1 = 2% \times 2.075 , \text{mL} = 0.02 \times 2.075 = 0.0415 , \text{mL} $$

• For Peak 2 (0.8%): $$ W_2 = 0.8% \times 2.075 , \text{mL} = 0.008 \times 2.075 = 0.0166 , \text{mL} $$

• For Peak 3 (1%): $$ W_3 = 1% \times 2.075 , \text{mL} = 0.01 \times 2.075 = 0.02075 , \text{mL} $$

3. Convert Weights to Equivalent Mass for Each Analysis

Convert the required amounts for LC-MS, NMR, and X-ray to an appropriate term (also consider unit conversions):

• LC-MS: $$ W_{\text{LC-MS}} = 1 , \text{ng} = 1 \times 10^{-6} , \text{g} $$

• NMR: $$ W_{\text{NMR}} = 10 , \text{mg} = 10 \times 10^{-3} , \text{g} = 1 \times 10^{-2} , \text{g} $$

• X-ray: $$ W_{\text{X-ray}} = 5 , \text{g} $$

4. Calculate Number of LC Runs for Each Analysis

Now, determine how many runs are required for each analysis based on the contribution of each peak.

• For LC-MS with Peak 1: $$ \text{Runs}_{\text{LC-MS}} = \frac{1 \times 10^{-6} , \text{g}}{0.0415 , \text{mL}} $$

• For NMR with Peak 2: $$ \text{Runs}_{\text{NMR}} = \frac{1 \times 10^{-2} , \text{g}}{0.0166 , \text{mL}} $$

• For X-ray with Peak 3: $$ \text{Runs}_{\text{X-ray}} = \frac{5 , \text{g}}{0.02075 , \text{mL}} $$

5. Calculate and Round Up the Total Required Runs

Finally, calculate these values and round up if needed.