An honours student needs to count the number of cells they have in a flask. They take an aliquot of the cells and dilute them 1:10 before loading 10 uL into a haemocytometer to perform a cell count. They count 4 quadrants and obtain the following counts for each quadrant: 262, 295, 307, 278.

Which of the following statements is the most correct?

Question

An honours student needs to count the number of cells they have in a flask. They take an aliquot of the cells and dilute them 1:10 before loading 10 uL into a haemocytometer to perform a cell count. They count 4 quadrants and obtain the following counts for each quadrant: 262, 295, 307, 278.

Which of the following statements is the most correct?

BlackTom AI · Accepted Answer

To approach this question, I will first restate the setup and identify the key numerical steps involved in converting a haemocytometer count to a concentration in the original flask.

The student made a 1:10 dilution, then loaded 10 μL into the haemocytometer and counted four corner/quadrant squares with counts: 262, 295, 307, 278.

Step 1: Calculate the average cell count per counted square.
- Add the four quadrant counts: 262 + 295 + 307 + 278 = 1142.
- Divide by the number of squares (4): 1142 / 4 = 285.5 cells per square on average.

Step 2: Apply the dilution factor.
- The dilution is 1:10, so the dilution factor (DF) is 10.

Step 3: Convert to concentration in the original flask.
- For haemocytometer counts, the standard conversion to cells per milliliter is: Concentration (cells/mL) = average count per square × DF × 10^4.
- Plugging in the numbers: 285.5 × 10 × 10^4 = 285.5 × 100,000 = 28,550,000 cells/mL, which is 2.855 × 10^7 cells/mL (approximately).

Now, let’s evaluate each answer choice.

Option 1: The cells in the original flask are at a concentration of 2.7 x 10^7 cells per mL
- This matches our calculation closely: 2.855 × 10^7 is in the 2.7 × 10^7 range when rounded to two significant figures. The use of a 1:10 dilution and the average count from the four quadrants are correctly incorporated. This option is numerically consistent with the standard formula and the data provided.

Option 2: They should take the cells from the original flask, perform a new 1:5 dilution and repeat the cell count
- A 1:5 dilution would imply a different DF (5 instead of 10), which would inflate or deflate the final concentration accordingly. Since the problem states the observed dilution was 1:10, recommending a 1:5 dilution contradicts the given procedure and would not be the correct next step for this calculation.

Option 3: They should take the cells from the original flask, perform a new 1:50 dilution and repeat the cell count
- A 1:50 dilution would use a DF of 50, leading to a final concentration that is off by a factor of 5 compared to the actual 1:10 dilution guidance. Repeating the count with a different dilution is not warranted unless the counts were out of a reliable range; given the provided data, this suggestion misaligns with the original setup and changes the calculation inappropriately.

Option 4: The cells in the original flask are at a concentration of 2.7 x 10^6 cells per mL
- This option differs by a factor of 10 from the calculated value (2.85 × 10^7). It would correspond to using a DF of 1 instead of 10, or misplacing a decimal in the final step. Since the dilution factor and the average count lead to roughly 2.85 × 10^7, this option undervalues the concentration by tenfold and is inconsistent with the math.

In summary, the calculation hinges on taking the average quadrant count (285.5), multiplying by the dilution factor (10), and applying the 10^4 conversion factor to get cells per mL. The first option aligns with that result, while the others either ignore the dilution, inappropriately change the dilution, or misstate the final magnitude.

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