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酵母菌浓度计算

Создано: 2 февраля 2025 г.

Отвечено с использованием O3 Mini High от Chat01

Вопрос

10ml培养基中有N个酵母菌，稀释100倍后采用16x25血细胞计数板计数，若某时刻中格细胞平均数量为25，求N的值？

Мысль

Taking a closer look

I’m translating and interpreting the problem, involving yeast cells in a 10 ml medium, 100-fold dilution, and counting on a specific hemocytometer grid.

Clarifying grid dimensions

I'm working through the possible interpretations of "16x25" for the hemocytometer's grid, considering either the grid area or chamber dimensions, and recalling typical hemocytometer characteristics.

Understanding grid structure

I'm mapping out the "16x25" grid dimensions on the hemocytometer "Blood cell counting board," likely indicating a 16 mm x 25 mm grid, crucial for determining cell concentration.

Piecing together dilution

I'm noting the average cell count of 25 in a 1 mm^2 square for a 1000-fold diluted sample, applying the hemocytometer's volume formula to back-calculate the original concentration.

Understanding hemocytometer grids

I’m clarifying that the "血细胞计数板" is a hemocytometer with a central grid divided into 16 and 25 squares, tailored for counting white blood cells.

Piecing together grid dimensions

I’m analyzing whether "16x25" refers to individual gridded cells or the overall grid layout, aiming to clarify for accurate cell concentration calculations.

Clarifying grid layout

OK, I’m sorting out if "16x25" denotes 16 squares by 25 squares, each with 0.25 mm sides. This configuration aligns with other observed hemocytometer layouts.

Piecing together

I’m focusing on the hemocytometer's central grid, subdivided into 16 and 25 smaller squares, to determine the counting method for leukocytes, adhering to standard counting protocols.

Mapping out cell count

I'm noting that for sparse cells, count in the central square's 25 small squares, then adjust using a conversion factor to determine the cell concentration accurately.

Analyzing grid areas

I’m identifying the specific grid sections in the counting chamber: 16 small squares and 25 small squares, to accurately calculate yeast cells in the dilution. This involves converting squares to cells.

Assessing grid specifics

I’m clarifying that the hemocytometer's "middle square" is the central grid, subdivided into 25 smaller squares, to calculate the yeast cell concentration accurately.

Validating volume calculations

I’m verifying that each of the 25 smaller squares in a hemocytometer's central grid has a volume of 0.004 mm^3, confirming the total volume as 1e-4 mL.

Calculating concentration

First, I determine the concentration of cells in the diluted sample, which is 2.5e5 cells/mL. Then, considering the 100-fold dilution factor, I ascertain the original concentration as 2.5e8 cells/mL.

Adjusting my approach

OK, let's consider that multiplying the central square count by the conversion factor of 10^4 gives a more accurate cell concentration estimate in the undiluted sample.

Clarifying grid dimensions

I’m noting that the center grid counts cells and has a volume 25 times greater than a single small square, based on specific hemocytometer configurations.

Verifying volume calculations

I confirm the volume of the middle grid in a 16x25 hemocytometer is 0.1 mm^3, consistent with the provided dilution factor and cell count.

Clarifying grid dynamics

It's interesting to see that the "16x25" hemocytometer likely refers to a compilation of 400 small squares, with "中格" possibly indicating a section or a particularly large square within.

Mapping out hemocytometer grids

I’m realizing that the "16格/25格" hemocytometer has a central 25-square grid with a total volume of 1 mm^3, efficiently calculating cell density in the diluted sample.

Calculating the result

Multiplying the diluted cell concentration by the dilution factor gives 25,000,000 cells/mL. Then, multiplying this by the sample volume results in 2.5 x 10^8 cells.

Reasoned about yeast concentration calculation，持续 38 秒

Ответ

在使用血细胞计数板计数时，我们通常利用中格（即中央那1 mm^2的区域，其深度为0.1 mm）的细胞数来计算细胞浓度。下面给出详细计算过程。

  1. 中格体积
    中格面积为1 mm^2，计数板的室深一般为0.1 mm，因此中格对应的体积

    V=1 mm2×0.1 mm=0.1 mm3.V = 1\,\text{mm}^2 \times 0.1\,\text{mm} = 0.1\,\text{mm}^3.

    注意单位换算：1 mL = 1 cm^3 = 1000 mm^3，所以

    V=0.1 mm3=0.1/1000 mL=1.0×10−4 mL.V = 0.1\,\text{mm}^3 = 0.1/1000\,\text{mL} = 1.0\times10^{-4}\,\text{mL}.

  2. 稀释后样品中的浓度
    题目中稀释100倍后，在中格中平均计数到25个细胞，这意味着在1.0×10^-^4 mL稀释液中有25个细胞。因此，稀释液的细胞浓度为

    C稀释液=25 个1.0×10−4 mL=2.5×105 个/mL.C_{\text{稀释液}} = \frac{25\,\text{个}}{1.0\times10^{-4}\,\text{mL}} = 2.5\times10^5\,\text{个/mL}.

  3. 原液浓度的计算
    因为样品稀释了100倍，所以原液（未经稀释）的浓度为

    C原液=2.5×105 个/mL×100=2.5×107 个/mL.C_{\text{原液}} = 2.5\times10^5\,\text{个/mL} \times 100 = 2.5\times10^7\,\text{个/mL}.

  4. 原液中酵母菌总数N
    原培养基体积为10 mL，则其中的细胞总数为

    N=C原液×10 mL=2.5×107 个/mL×10 mL=2.5×108 个.N = C_{\text{原液}} \times 10\,\text{mL} = 2.5\times10^7\,\text{个/mL} \times 10\,\text{mL} = 2.5\times10^8\,\text{个}.

因此，10 mL培养基中含有酵母菌

N=2.5×108 个.N = 2.5\times10^8\,\text{个}.

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