I need help doing the work, I think something might be wrong.
How many glucose molecules does an E coli cell contain if it has an internal glucose concentration of 1.0 mM. The E coli is a cylinder that is 2 micrometers long and 1 micrometer in diameter.
pi*r^2*h
3.14 * .00005^2 * .0002 = 1.57x10^-12
1.57x10^-12 cm3 = 1.57 x 10 ^ -15 L
1 x 10 ^-3 moles/Liter x 1.57 x 10^-15 L = 1.57 x 10 ^ -18 moles of glucose
1.57 x 10^-18 * 6.02 x 10^ 23 = 945, 140 glucose molecules (?)
That looks ok to me.
To calculate the number of glucose molecules an E. coli cell contains, you need to follow these steps:
1. Determine the volume of the E. coli cell:
The formula for the volume of a cylinder is V = π * r^2 * h, where V is the volume, π is a constant (approximately 3.14), r is the radius, and h is the height or length. In this case, the length is given as 2 micrometers and the diameter (which is twice the radius) is given as 1 micrometer. Convert the measurements into centimeters to maintain consistent units. Thus, the radius (r) becomes 0.00005 cm and the length (h) becomes 0.0002 cm.
V = 3.14 * (0.00005)^2 * 0.0002
V = 1.57 x 10^-12 cm^3
2. Convert the volume of the E. coli cell to liters:
Since the concentration of glucose is given in millimoles per liter (mM), it's necessary to have the volume in liters. Use the conversion factor that 1 cm^3 is equal to 1 x 10^-3 liters.
1.57 x 10^-12 cm^3 = 1.57 x 10^-15 L
3. Calculate the number of moles of glucose:
The given glucose concentration is 1.0 mM, which means there is 1.0 mole of glucose in 1 liter. Multiply the concentration by the volume in liters to find the number of moles of glucose.
1.0 moles/Liter * 1.57 x 10^-15 L = 1.57 x 10^-15 moles of glucose
4. Convert moles to molecules:
One mole of any substance contains 6.02 x 10^23 molecules (Avogadro's number). Multiply the number of moles by Avogadro's number to calculate the total number of glucose molecules.
1.57 x 10^-15 moles * 6.02 x 10^23 = 9.45 x 10^8 glucose molecules
Therefore, an E. coli cell with an internal glucose concentration of 1.0 mM contains approximately 9.45 x 10^8 glucose molecules.