If the water molecules in 5.70 g of water (H2O) were distributed uniformly over the surface of the Earth, how many such molecules would there be on 1.40 cm2 of the Earth's surface?
-Molar mass Hydrogen gas(H2)=2.02 g/mol
-Molar mass Oxygen gas (O2) = 32.0 g/mol
-Radius of Earth = 6370 km
-Avogadro's number = 6.02 ¡Á 1023 particles/mol
Thanks in advance !!
5.7g * 1mole/18.02g * 6.02*10^23 molecules/mole = 1.905*10^23 molecules
Now, multiply that by the fraction of the earth's surface, and you get
1.905*10^23 * 1.4cm^2/(5.1*10^18 cm^2)
= 52294 molecules
To calculate the number of water molecules on a given area of the Earth's surface, we need to follow these steps:
Step 1: Calculate the number of moles of water in 5.70 g of H2O.
Step 2: Use the molar ratio of H2O to determine the number of moles of water molecules.
Step 3: Convert moles to molecules using Avogadro's number.
Step 4: Calculate the total surface area of the Earth.
Step 5: Divide the total number of water molecules by the total surface area to find the number of water molecules per 1.40 cm².
Let's calculate each step:
Step 1: Calculate the number of moles of water in 5.70 g of H2O.
Molar mass of H2O = (2.02 g/mol * 2) + 16.0 g/mol = 18.04 g/mol
Number of moles of H2O = (mass of H2O) / (molar mass of H2O)
= 5.70 g / 18.04 g/mol
≈ 0.316 mol
Step 2: Use the molar ratio of H2O to determine the number of moles of water molecules.
Since one mole of H2O contains 6.02 × 10²³ molecules, the number of moles of water molecules is equal to the number of moles of water.
Number of moles of water molecules = 0.316 mol
Step 3: Convert moles to molecules using Avogadro's number.
Number of molecules of water = (number of moles of water molecules) * (Avogadro's number)
= 0.316 mol * 6.02 × 10²³ molecules/mol
≈ 1.90 × 10²³ molecules
Step 4: Calculate the total surface area of the Earth.
The surface area of a sphere can be calculated using the formula:
Surface area = 4πr²
Where r is the radius of the Earth, which is 6370 km.
Surface area of the Earth = 4π(6370 km)²
The unit of the radius must match with the unit of the surface area calculation. We'll convert kilometers to centimeters:
Surface area of the Earth = 4π(6370 km * 100,000 cm/km)²
= 4π(6.37 × 10⁸ cm)²
≈ 5.09 × 10²⁰ cm²
Step 5: Divide the total number of water molecules by the total surface area to find the number of water molecules per 1.40 cm².
Number of water molecules per 1.40 cm² = (number of water molecules) / (surface area of the Earth)
= (1.90 × 10²³ molecules) / (5.09 × 10²⁰ cm²)
≈ 3.73 × 10² molecules
Therefore, there would be approximately 3.73 × 10² water molecules on 1.40 cm² of the Earth's surface.
To find the number of water molecules on 1.40 cm2 of the Earth's surface, we need to calculate the number of moles of water in 5.70 g of water and then convert it to the number of water molecules.
To calculate the number of moles of water, we need to know the molar mass of water. The molar mass of water (H2O) is the sum of the molar masses of its constituent elements, hydrogen and oxygen.
Molar mass of hydrogen gas (H2) = 2.02 g/mol
Molar mass of oxygen gas (O2) = 32.0 g/mol
Since water (H2O) has two hydrogen atoms and one oxygen atom, the molar mass of water is:
Molar mass of water (H2O) = 2 * Molar mass of hydrogen + Molar mass of oxygen
= 2 * 2.02 g/mol + 32.0 g/mol
= 4.04 g/mol + 32.0 g/mol
= 36.04 g/mol
Now, we can calculate the number of moles of water in 5.70 g of water using the formula:
Number of moles = Mass of sample / Molar mass
Number of moles of water = 5.70 g / 36.04 g/mol
= 0.1583 mol
Next, we need to convert the number of moles of water to the number of water molecules. To do this, we'll use Avogadro's number.
Avogadro's number is 6.02 × 10^23 particles/mol.
Number of water molecules = Number of moles of water * Avogadro's number
= 0.1583 mol * 6.02 × 10^23 particles/mol
= 9.51 × 10^22 particles
Now, we know that 5.70 g of water contains approximately 9.51 × 10^22 water molecules.
To find the number of water molecules on 1.40 cm2 of the Earth's surface, we need to calculate the value for the entire surface area of the Earth and then divide it by the area of 1.40 cm2.
The surface area of a sphere can be calculated using the formula:
Surface area = 4 * π * (radius)^2
Radius of the Earth = 6370 km = 6370 × 10^5 cm
Surface area of the Earth = 4 * π * (6370 × 10^5 cm)^2
Now we can calculate the number of water molecules on 1.40 cm2 of the Earth's surface by dividing the total number of water molecules on the Earth's surface by the surface area of the Earth.
Number of water molecules on 1.40 cm2 of the Earth's surface = (Number of water molecules) / (Surface area of the Earth) * (Area of 1.40 cm2)