What is the formula for CoCl2 with 45.5 percent water?
let x = number mols H2O/mol CoCl2.
%H2O = 18.015x/(18.015x + molar mass CoCl2)
Solve for x and the formula is
CoCl2.xH2O
To determine the formula for CoCl2 with 45.5% water, we need to consider the ratio between the cobalt chloride (CoCl2) and the water present. The formula will be determined by dividing the number of moles of water by the number of moles of cobalt chloride.
First, let us calculate the number of moles of water:
1. Convert the given percentage of water to grams. Assuming we have 100 grams of the compound in total, 45.5% of that would be water.
Mass of water = (45.5/100) * 100 g = 45.5 g
2. Convert the mass of water to moles. The molar mass of water, H2O, is 18 g/mol.
Moles of water = Mass of water / Molar mass of water
= 45.5 g / 18 g/mol
≈ 2.528 moles
Next, let's calculate the number of moles of cobalt chloride (CoCl2):
3. Determine the mass of CoCl2 by subtracting the mass of water from the total mass:
Mass of CoCl2 = Total mass - Mass of water
= 100 g - 45.5 g
= 54.5 g
4. Convert the mass of CoCl2 to moles. The molar mass of CoCl2 is 129.84 g/mol.
Moles of CoCl2 = Mass of CoCl2 / Molar mass of CoCl2
= 54.5 g / 129.84 g/mol
≈ 0.420 moles
Finally, determine the ratio between the moles of water and cobalt chloride:
5. Divide the moles of water by the moles of CoCl2 to determine the mole ratio:
Moles ratio = Moles of water / Moles of CoCl2
= 2.528 moles / 0.420 moles
≈ 6.02
Therefore, the formula for CoCl2 with 45.5% water is CoCl2 · 6H2O, which represents one formula unit of cobalt chloride combined with six molecules of water.
To determine the formula for CoCl2 with 45.5 percent water, we need to analyze the given information and calculate the number of water molecules (H2O) relative to cobalt chloride (CoCl2).
Let's begin by assuming we have 100 grams of the compound. Therefore, 45.5 percent water corresponds to 45.5 grams of H2O.
Next, we need to convert the mass of water (H2O) to moles. To do this, we divide the mass of water by its molar mass. The molar mass of water (H2O) is approximately 18 g/mol (2 grams for hydrogen and 16 grams for oxygen).
Moles of H2O = Mass of H2O / Molar mass of H2O
= 45.5 g / 18 g/mol
= 2.5278 mol
Now, we need to determine the moles of cobalt chloride (CoCl2) in the compound. Since the compound contains only one cobalt atom in each formula unit, the number of moles of cobalt is equal to the number of moles of cobalt chloride.
However, since cobalt chloride (CoCl2) has two chlorine (Cl) atoms per formula unit, the moles of chlorine are doubled compared to the moles of cobalt chloride.
To confirm this, we can use the Law of Conservation of Mass. The mass of chlorine will be equal to the mass of water.
Mass of chlorine = Mass of water = 45.5 g
Now, we need to convert the mass of chlorine to moles. The molar mass of chlorine (Cl) is approximately 35.5 g/mol.
Moles of Cl = Mass of Cl / Molar mass of Cl
= 45.5 g / 35.5 g/mol
= 1.2824 mol
Since there are two moles of chlorine for every mole of cobalt chloride, we divide the moles of chlorine by 2 to find the moles of cobalt chloride.
Moles of CoCl2 = Moles of Cl / 2
= 1.2824 mol / 2
= 0.6412 mol
Now, the ratio between the moles of water and moles of cobalt chloride can be determined by dividing the moles of water by the moles of cobalt chloride.
Ratio of moles of H2O to CoCl2 = Moles of H2O / Moles of CoCl2
= 2.5278 mol / 0.6412 mol
= 3.945
Rounding to the nearest whole number, we find that the ratio is approximately 4. Therefore, the formula for CoCl2 with 45.5 percent water is CoCl2·4H2O.