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Chapter 12: Problem 12

Find the mass of 1.6 mol of magnesium, Mg. How many atoms are present in such a sample?

Short Answer

Expert verified
The mass of 1.6 mol of magnesium is 38.888 g. There are \(9.6352 \times 10^{23}\) atoms in this sample.

Step by step solution

01

- Find the molar mass of magnesium

The molar mass of magnesium (Mg) can be found on the periodic table. Magnesium has a molar mass of 24.305 g/mol.
02

- Calculate the mass of magnesium

Use the formula: \[ \text{mass} = \text{number of moles} \times \text{molar mass} \] Given 1.6 mol of Mg and molar mass of 24.305 g/mol: \[ \text{mass} = 1.6 \text{ mol} \times 24.305 \text{ g/mol} = 38.888 \text{ g} \]
03

- Use Avogadro's number to find the number of atoms

The number of atoms in a mole is given by Avogadro's number, which is \(6.022 \times 10^{23}\) atoms/mol. Multiply the number of moles by Avogadro's number. \[ \text{number of atoms} = 1.6 \text{ mol} \times 6.022 \times 10^{23} \text{ atoms/mol} = 9.6352 \times 10^{23} \text{ atoms} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Magnesium Molar Mass
Every element has a molar mass, which tells you the mass of one mole of that element. You can find this information on the periodic table.
For magnesium (Mg), the molar mass is 24.305 grams per mole (g/mol). This means one mole of magnesium weighs exactly 24.305 grams.
Understanding how to find and use molar mass is crucial in solving many chemistry problems.
Always remember to check the periodic table for accurate values when performing molar mass calculations.
Avogadro's Number
Avogadro's number is a constant, which represents the number of atoms or molecules in one mole of any substance.
The value of Avogadro's number is approximately: \( 6.022 \times 10^{23} \text{ atoms/mol} \).
This huge number is incredibly useful in chemistry to convert between moles and the actual number of atoms or molecules.
For example, if you have 1 mole of magnesium, it means you have \( 6.022 \times 10^{23} \) magnesium atoms.
Mole to Atoms Conversion
To convert moles of a substance to atoms, you need to use Avogadro's number.
Here's the simple formula:
  • Number of atoms = Number of moles \( \times 6.022 \times 10^{23} \text{ atoms/mol} \)

For example, if you have 1.6 moles of magnesium, you can find the number of atoms by multiplying 1.6 by \( 6.022 \times 10^{23} \).
It looks like this in calculation: \( 1.6 \text{ mol} \times 6.022 \times 10^{23} \text{ atoms/mol} = 9.6352 \times 10^{23} \text{ atoms} \).
This step is essential for linking the concept of moles to actual quantities of atoms.
Mass Calculation
To find the mass of a substance when you know how many moles you have, you use the molar mass of that substance.
The formula is simple:
  • mass = number of moles \( \times \text{ molar mass (g/mol)} \)

For instance, if you have 1.6 moles of magnesium and its molar mass is 24.305 g/mol, you can calculate the mass as: \( 1.6 \text{ mol} \times 24.305 \text{ g/mol} = 38.888 \text{ g} \).
This formula lets you easily find out how much a certain amount of moles of any substance will weigh.

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