A cylindrical glass of water (H2O) has a radius of 6.12 cm and a height of 9.91 cm. The density of water is 1.00 g/cm3. How many moles of water are contained in the glass?
To find the number of moles of water in the glass, we need to know the mass of water in grams and the molar mass of water.
First, let's calculate the volume of the cylindrical glass. The volume of a cylinder can be calculated using the formula V = πr^2h, where r is the radius and h is the height. So, substituting the given values:
V = π(6.12 cm)^2 × 9.91 cm
V ≈ 1159.802 cm^3
The density of water is given to be 1.00 g/cm^3, so the mass of water can be calculated using the formula mass = density × volume.
mass = 1.00 g/cm^3 × 1159.802 cm^3
mass ≈ 1159.802 g
The molar mass of water (H2O) is the sum of the atomic masses of two hydrogen atoms (H) and one oxygen atom (O). The atomic masses can be found on the periodic table. The atomic mass of hydrogen is approximately 1.01 g/mol, and the atomic mass of oxygen is approximately 16.00 g/mol.
molar mass of water = 2 × atomic mass of hydrogen + atomic mass of oxygen
molar mass of water ≈ 2 × 1.01 g/mol + 16.00 g/mol ≈ 18.02 g/mol
Finally, to find the number of moles of water, we divide the mass of water by the molar mass of water:
moles = mass / molar mass
moles ≈ 1159.802 g / 18.02 g/mol ≈ 64.35 mol
Therefore, there are approximately 64.35 moles of water in the glass.