A cylindrical glass of water (H2O) has a radius of 3.49 cm and a height of 9.85 cm. The density of water is 1.00 g/cm3. How many moles of water are contained in the glass?
To calculate the number of moles of water in the glass, we need to use the formula:
moles = mass / molar mass
Let's break it down step-by-step:
Step 1: Calculate the volume of the cylindrical glass.
The volume of a cylinder is given by the formula:
volume = π * radius^2 * height
Using the given values, substitute them into the formula:
volume = π * (3.49 cm)^2 * 9.85 cm
Step 2: Convert the volume from cm^3 to liters.
1 liter is equal to 1000 cm^3, so we need to divide the volume by 1000:
volume = (π * (3.49 cm)^2 * 9.85 cm) / 1000 = [insert numerical calculation]
Step 3: Calculate the mass of the water using the density formula.
The density formula is:
density = mass / volume
Rearranging the formula, we get:
mass = density * volume
Substitute the given density value and the calculated volume:
mass = 1.00 g/cm^3 * [insert volume from Step 2]
Step 4: Convert mass from grams to moles.
To convert grams to moles, we need to use the molar mass of water, which is approximately 18.02 g/mol. We divide the mass by the molar mass:
moles = mass / molar mass
Substitute the calculated mass and the molar mass:
moles = [insert mass from Step 3] / 18.02 g/mol
Finally, calculate the value to determine the number of moles of water contained in the glass.
To find the number of moles of water contained in the glass, we need to use the following formula:
moles = mass / molar mass
First, let's calculate the mass of the water in the glass:
volume of water = π * (radius)² * height
mass = volume of water * density
The molar mass of water (H2O) is approximately 18.01528 g/mol.
Now, let's calculate step by step:
1. Calculate the volume of water in the glass:
volume of water = π * (3.49 cm)² * 9.85 cm
2. Calculate the mass of the water:
mass = volume of water * density
3. Convert the mass of water from grams to moles:
moles = mass / molar mass (18.01528 g/mol)
By following these steps, we can find the number of moles of water contained in the glass.