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. Really stuck on this one, thanks for the help!
The volume of a cylinder is pi*r^2*h.
You know pi, change 1 micrometer to cm and take half to get radius, change 2 micrometers to cm for the height. Calculate volume which will be in cc. Change to liters knowing that 1000 cc = 1 L.
1 mM = 1 millimolar = 1 x 10^-3 Molar = 1 x 10^-3 moles/Liter.
Multiply moles/L x Liters (volume) to obtain moles of glucose then calculate number of molecules knowing that there are 6.02 x 10^23 molecules in 1 mole.
Post your work if you get stuck.
To calculate the number of glucose molecules an E.coli cell contains, we need to consider both the volume of the cell and the concentration of glucose inside it.
First, let's calculate the volume of the E.coli cell. The formula for the volume of a cylinder is V = πr^2h, where "r" represents the radius of the cylinder and "h" represents the height. In this case, the E.coli is a cylinder-shaped cell that is 2 micrometers long and 0.5 micrometers in radius (since the diameter is given as 1 micrometer).
Using the formula, the volume of the E.coli cell is:
V = π(0.5 μm)^2 * 2 μm
V ≈ 1.57 μm^3 (rounded to two decimal places)
Next, we need to convert this volume to liters since the glucose concentration is given in millimoles per liter (mM). We know that 1 μm^3 is equivalent to 1 x 10^-15 liters.
Volume in liters = (Volume in cubic micrometers) x (1 x 10^-15 liters / 1 μm^3)
Volume in liters = 1.57 μm^3 * 1 x 10^-15 liters / 1 μm^3
Volume in liters = 1.57 x 10^-15 liters
Now, we can calculate the number of glucose molecules in the E.coli cell using the concentration of glucose mentioned in the question (1.0 mM). The Avogadro's number (6.022 x 10^23) represents the number of molecules in one mole of a substance.
Number of molecules = (Volume in liters) x (Concentration in moles per liter) x (Avogadro's number)
Number of molecules = 1.57 x 10^-15 liters * 1.0 mM * 6.022 x 10^23 molecules per mole
Number of molecules ≈ 9.45 x 10^5 molecules
Therefore, an E.coli cell with an internal glucose concentration of 1.0 mM contains approximately 9.45 x 10^5 glucose molecules.