Final answer:
To find the mass of the bacterium, use the formula for the volume of a sphere, multiply by the density of water to get the mass in kg.
Convert grams to kilograms by dividing by 1000. Use Avogadro's number to convert kg to kilodaltons.
Calculate the number of Staphylococcus aureus cells needed to circle the Earth by dividing the circumference of the Earth by the diameter of the bacterium.
Find the surface area of the bacterium using the formula for the surface area of a sphere, and calculate the number of phospholipid molecules in the plasma membrane by multiplying the area per lipid molecule by the surface area of the bacterium.
Step-by-step explanation:
To find the mass of the bacterium, we can calculate its volume using the formula for the volume of a sphere: V = (4/3)×πr^3. Given that the diameter of the bacterium is 1.0 μm, the radius (r) is 0.5 μm (since radius = diameter/2 = 1.0 μm/2). Plugging this value into the volume formula, we get V = (4/3)×π(0.5 μm)^3. To find the mass, we can multiply the volume by the density of water, which is 1 g/mL.
To convert grams to kilograms, we divide by 1000. Thus, the mass of the bacterium in kg is (4/3)×π(0.5 μm)^3 × 1 g/mL ÷ 1000 = (4/3)×π(0.5 μm)^3 × 10-3 kg.
To convert kg to kilodaltons (kD), we can use Avogadro's number (6.022x10^23). The molar mass of water is approximately 18 g/mol, so the number of water molecules in a kg is 103 mol/kg × 6.022x10^23 molecules/mol = 6.022x10^26 molecules/kg. To find the number of water molecules in the bacterium, we can multiply this value by the mass of the bacterium in kg.
To calculate how many Staphylococcus aureus cells would be needed to circle the Earth, we need to find the circumference of the Earth and divide it by the diameter of the bacterium. The circumference of the Earth is 2×π×6378.1 km, and the diameter of the bacterium is 1 μm. Dividing the circumference by the diameter gives us the number of cells needed to form a complete circle around the Earth.
The surface area of the bacterium can be found using the formula for the surface area of a sphere: A = 4×πr^2. Plugging in the radius, we get A = 4×π(0.5 μm)^2. To convert μm^2 to m^2, we divide by 10^12.
To find the number of phospholipid molecules in the bacterium's plasma membrane, we need to know the surface area of the membrane. Based on the given information, the area of each lipid molecule is 0.50 nm^2. Assuming the plasma membrane is a double layer, we can multiply the area per lipid molecule by the surface area of the bacterium to get the total number of lipid molecules in the membrane.