a pure sample of metal has a mass of .164g and confains 1.90 x 10^21 atoms. Calculate the molar mass of this metal

To calculate the molar mass of the metal, we will use the following approach:

### Steps:
1. **Find the number of moles of atoms:**

   The number of moles of atoms can be calculated using the formula:
   \[
   \text{{moles}} = \frac{\text{{number of atoms}}}{\text{{Avogadro's number}}}
   \]
   where Avogadro's number is \(6.022 \times 10^{23} \, \text{atoms/mol}\).

2. **Calculate the molar mass:**

   The molar mass (\(M\)) of the metal can be calculated using the relation:
   \[
   M = \frac{\text{{mass of the sample}}}{\text{{moles of atoms}}}
   \]
   
### Given Data:
- Mass of the sample: \(0.164 \, \text{g}\)
- Number of atoms: \(1.90 \times 10^{21} \, \text{atoms}\)
- Avogadro's number: \(6.022 \times 10^{23} \, \text{atoms/mol}\)

Now, let's compute the molar mass.

### Step 1: Calculate the number of moles of atoms:
\[
\text{moles} = \frac{1.90 \times 10^{21} \, \text{atoms}}{6.022 \times 10^{23} \, \text{atoms/mol}}
\]

Let me calculate this.The number of moles of atoms is approximately \(0.00316 \, \text{mol}\).

### Step 2: Calculate the molar mass:
Now, using the formula:
\[
M = \frac{\text{mass of the sample}}{\text{moles of atoms}}
\]
\[
M = \frac{0.164 \, \text{g}}{0.00316 \, \text{mol}}
\]

Let me calculate this next.The molar mass of the metal is approximately \(51.98 \, \text{g/mol}\).

Would you like any further details or explanations?

Here are some related questions you could explore:
1. How does Avogadro's number relate to molar mass?
2. What other methods can be used to determine the molar mass of a metal?
3. How does the molar mass affect a metal’s physical properties?
4. What is the significance of molar mass in chemical reactions?
5. Can molar mass vary with isotopic composition?

**Tip:** Molar mass can be a crucial factor in determining the metal's identity, as each element has a unique molar mass!

A pure sample of metal has a mass of 0.164g and contains 1.90 x 10^21 atoms. Calculate the molar mass of this metal.

Learn how to calculate the molar mass of a metal sample weighing 0.164g with 1.90 x 10^21 atoms. This problem uses key concepts such as moles, Avogadro's number, and molar mass calculation. Suitable for high school students in Grades 10-12.

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