The chloride of an unknown metal is believed to have the formula MCl 3 . A 2.395-g sample of the compound contains 3.606×10 -2 mol Cl. Find the atomic mass of M.

Hey, everyone. And welcome back to another video. The chloride of an unknown metal is believed to have the formula MC L three A 2.395 g sample of the compound contains 3.606 multiplied by 10, the negative second moles of chlorine by the atomic mass of M. And we are given for answer choices A 94.05 B 106.3 C 92.93 and D 107.6 all given in grams per mole. So now there are multiple ways to solve this problem. But in my opinion, the easiest one is the following. We can take our compound and we can deal with psychometry. Let's suppose that we take one mole of our compound. And what we know is that one mole of this compound has three moles of chlorine, right? How do we know that? Well, essentially if we look at psychometry, if we take one unit of MC L three, it has three chlorine atoms or specifically speaking, because it's a metal, right? M is a metal, those be the chloride anions. So we can be more accurate. Now, what we want to do is essentially convert from moles of chlorine to moles of our compound. So the number of moles of MC three is essentially three times lower. How do we know that we take 3.606 multiplied by, since the negative second, most of chlorine, in this case, the chloride anion and we can include our conversion factor. On the bottom, we use most of chloride because we want to cancel the units out. And on top, we use most of MC L spray, there's a 1 to 3 ratio. And if we do the math, we get 1.202 multiplied by 10th of the power of negative second moles. Now we have the number of moles of our compound. We have our mass, we can find a molar mass of MC L three to find the molar mass, we simply take the mass, right. So that would be 2.395 g. And we are going to divide that by the number of moles that we have identified. So we divide the two numbers, let's calculate the result. Now, the result that we get is a 199.25. So this is the total molar mass of our compound, but our compound has three units of chloride. So to identify the molar mass of the metal M, we're going to take the total molar mass 199.25. And we're going to subtract the total molar mass of the chloride anions. So, if we have three of them, we're multiplying three by the molar mass of chlorine, that'd be 35.45 g per mole. And eventually, this gives us a difference of 92.93 g per mole, which is the molar mass of the metal M. And this corresponds to the answer choice C. That would be it for today. And thank you for watching.

Ch.3 - Molecules and Compounds

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Ch.3 - Molecules and Compounds

Problem 127

Chapter 3, Problem 127

The chloride of an unknown metal is believed to have the formula MCl₃. A 2.395-g sample of the compound contains 3.606×10^-2 mol Cl. Find the atomic mass of M.

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Determine the moles of metal chloride in the sample. Since the formula of the metal chloride is MCl3, which means each mole of MCl3 contains 3 moles of Cl. Use the given moles of Cl to find the moles of MCl3 by dividing the moles of Cl by 3.

Calculate the molar mass of MCl3. Since you know the mass of the MCl3 sample and the moles of MCl3, use the formula: Molar mass = Mass of the sample / Moles of MCl3.

Write the formula for the molar mass of MCl3 in terms of the atomic mass of M (M_m) and the molar mass of Cl (Cl_m). The formula is Molar mass of MCl3 = M_m + 3 * Cl_m.

Set up the equation from step 2 equal to the expression from step 3. This will allow you to solve for the atomic mass of M (M_m).

Solve the equation for M_m (the atomic mass of M) by isolating M_m on one side of the equation.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Molar Mass and Moles

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). The number of moles of a substance can be calculated using the formula: moles = mass (g) / molar mass (g/mol). In this question, understanding how to convert between mass and moles is essential for determining the atomic mass of the unknown metal.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions based on the conservation of mass. In this case, the formula MCl3 indicates that one mole of the metal M combines with three moles of chlorine (Cl). This relationship is crucial for determining the amount of M in the compound based on the moles of Cl provided.

Empirical and Molecular Formulas

The empirical formula represents the simplest whole-number ratio of elements in a compound, while the molecular formula shows the actual number of atoms of each element. For MCl3, the empirical formula is the same as the molecular formula. Understanding how to derive the molecular formula from the mass and moles of the components is key to finding the atomic mass of the unknown metal M.

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The chloride of an unknown metal is believed to have the formula MCl3. A 2.395-g sample of the compound contains 3.606×10-2 mol Cl. Find the atomic mass of M.

Verified Solution

Key Concepts

Molar Mass and Moles

Stoichiometry

Empirical and Molecular Formulas

The chloride of an unknown metal is believed to have the formula MCl₃. A 2.395-g sample of the compound contains 3.606×10^-2 mol Cl. Find the atomic mass of M.