an unknown metal reacts with chlorine to produce 6.84 g of metal chloride. when metal chloride dissolves in 100 mL of solvent the metal ion concentration is 0.43 M. What is the unknown metal?
To determine the identity of the unknown metal, we need to use the given information and some chemical principles.
Let's break down the steps involved in solving this problem:
1. Calculate the moles of metal chloride (MCl2) produced:
- The molar mass of chlorine (Cl2) is approximately 70.9 g/mol. So, the moles of Cl2 reacted can be calculated by dividing the given mass (6.84 g) by the molar mass.
- Moles of Cl2 = 6.84 g / 70.9 g/mol
2. Determine the moles of metal (M) in the metal chloride:
- Since the metal chloride (MCl2) is produced from 1 mole of metal (M) and 2 moles of chlorine (Cl2), the number of moles of metal equals half the moles of the metal chloride.
- Moles of M = (1/2) * Moles of Cl2
3. Calculate the number of moles of metal ions (M^+) in the solution:
- Given that the metal ion concentration is 0.43 M and the volume of the solvent is 100 mL (0.1 L), we can calculate the moles of metal ions.
- Moles of M^+ = Metal ion concentration * Volume of solution (in L)
4. Compare the moles from Step 2 and Step 3 to identify the unknown metal:
- If the moles of metal (M) from Step 2 are the same as the moles of metal ions (M^+) from Step 3, then the molar ratio is 1:1, indicating that the metal chloride formula is MCl2. This would suggest a compound like magnesium chloride (MgCl2), where the metal ion concentration would also be 0.43 M.
By following these steps, you can determine the identity of the unknown metal by comparing the moles of metal (M) with the moles of metal ions (M^+) in the solution.
To find the unknown metal, we need to calculate the number of moles of metal chloride formed and compare it with the initial amount of metal.
Step 1: Calculate the number of moles of metal chloride formed
We know that the molar mass of any metal chloride is the sum of the atomic masses of the metal and chlorine. Let's denote the unknown metal as M, so the molar mass of MCl is M + 35.45 g/mol.
First, we need to find the number of moles of metal chloride produced. We can use the formula:
moles of metal chloride = mass of metal chloride / molar mass of metal chloride
Given that the mass of metal chloride produced is 6.84 g, and the molar mass of MCl is M + 35.45 g/mol, the number of moles of metal chloride can be calculated as:
moles of metal chloride = 6.84 g / (M + 35.45 g/mol)
Step 2: Calculate the number of moles of metal
The metal ion concentration in the solution after dissolving the metal chloride is given as 0.43 M, which represents the number of moles of metal ions per liter of solvent.
To calculate the number of moles of metal in the 100 mL (0.1 L) solvent, we can use the formula:
moles of metal = concentration of metal ion × volume of solution (in liters)
moles of metal = 0.43 M × 0.1 L
Step 3: Equate the number of moles of metal chloride and metal
Since the reaction is 1:1 (1 mole of metal corresponds to 1 mole of metal chloride), we can equate the two quantities:
moles of metal chloride = moles of metal
6.84 g / (M + 35.45 g/mol) = 0.43 M × 0.1 L
Now we can solve this equation to find the value of M, which will represent the unknown metal.