Final answer:
The formula of the metal chloride will be MCl5.
Step-by-step explanation:
The formula of the metal chloride can be determined by using the concept of vapor density. The formula of a compound can be determined based on the ratio of the masses of its components. In this case, we have the vapour density of the chloride which is 94.8. The vapour density of a compound is the ratio of the molar mass of the compound to the molar mass of the gas.
We are given that the compound contains 74.75% chlorine. From this information, we can calculate the molar mass of the compound as follows:
- Assume 100 grams of the compound.
- The mass of chlorine in the compound is 74.75 grams (74.75% of 100).
Now, we can determine the mass of the metal in the compound by subtracting the mass of chlorine from the total mass:
- Total mass - Mass of chlorine = Mass of metal
- 100 grams - 74.75 grams = 25.25 grams
Since we know the mass of the metal and the molar mass of the compound, we can calculate the number of moles of the metal in the compound:
- Number of moles = Mass of metal / Molar mass of the compound
- Number of moles = 25.25 grams / (Molar mass of the compound)
Next, we can calculate the number of moles of chlorine in the compound:
- Number of moles of chlorine = Mass of chlorine / Molar mass of chlorine
- Number of moles of chlorine = 74.75 grams / (35.45 g/mol)
Finally, we can determine the ratio of the moles of metal to the moles of chlorine in the compound:
- Ratio = Moles of metal / Moles of chlorine
- Ratio = (25.25 grams / (Molar mass of the compound)) / (74.75 grams / (35.45 g/mol))
From the given information, we know that the ratio of chlorine to the metal is 74.75%, which means that the ratio of moles of chlorine to the moles of metal is also 74.75%. Therefore, the ratio of moles is equal to the ratio of masses:
- Ratio = Moles of metal / Moles of chlorine
- Ratio = (25.25 grams / (Molar mass of the compound)) / (74.75 grams / (35.45 g/mol))
- 74.75% = (25.25 grams / (Molar mass of the compound)) / (74.75 grams / (35.45 g/mol))
Solve this equation to find the molar mass of the compound:
- Multiplying both sides of the equation by (74.75 grams / (35.45 g/mol)) gives:
- (74.75 grams / (35.45 g/mol)) * (25.25 grams / (Molar mass of the compound)) = 74.75%
- Simplifying the left side of the equation gives:
- 25.25 grams / (Molar mass of the compound) = 74.75%
- Dividing both sides of the equation by 74.75% gives:
- 25.25 grams / (Molar mass of the compound) = 1
- Therefore, the molar mass of the compound is 25.25 grams.
Since the vapour density is a ratio of the molar mass of the compound to the molar mass of the gas, we can determine the molar mass of the compound:
- Vapour density = Molar mass of the compound / Molar mass of the gas
- Substituting the given values, we have:
- 94.8 = 25.25 grams / (Molar mass of the gas)
- Solving for the molar mass of the gas:
- Molar mass of the gas = 25.25 grams / 94.8
- Molar mass of the gas = 0.266 g/mol
Now, we can determine the molar mass of the metal chloride:
- Molar mass of the metal chloride = Molar mass of the gas / Ratio of moles of metal to moles of chlorine
- Substituting the values, we have:
- Molar mass of the metal chloride = 0.266 g/mol / (25.25 grams / (Molar mass of the compound))
- To simplify the calculation, we can assume the formula of the metal chloride as MClx, where x is the oxidation number of the metal.
- Therefore, the formula of the metal chloride will be MCl5.