Question

1.According to the periodic table, a single (1 exactly) carbon atom has a mass of 12.011 amu. What is the mass of a single carbon atom in grams?

2. How many carbon atoms does it take to equal 12.011 grams? Complete the dimensional analysis set up provided for you (Hint: Your answer to question 1 can help answer this question). (Round to 3 sig figs)

3. According to the periodic table, a single phosphorus atom has a mass of 30.973 amu. What is the mass of a single phosphorus atom in grams? (Hint: similar to question 1)

4. How many phosphorus atoms does it take to equal 30.973 grams? (Hint: similar to question 2). (Round to 3 sig figs)

5. What is the mass (in amu) of one atom of aluminum (Al)?

6. If you had 6.022 x 1023 atoms of aluminum, what mass of aluminum (in g) would you have?

7. The value that you calculated in question 6 is called a molar mass. Using the fact that “molar” is similar to the word “mole,” define the term “molar mass” in your own words.

Answer 1

1) A single carbon atom has a mass of 12.011 amu.

We know, 1 amu = 1.660539040 × 10⁻²⁴ gram

The mass of a single carbon atom in grams = 12.011 amu × (1.660539040 × 10⁻²⁴ gram / 1 amu) = 1.992646547 × 10⁻²³ gram

• The mass of a single carbon atom in grams = 1.992646547 × 10⁻²³ grams.

2) For 1.992646547 × 10⁻²³ gram, it takes 1 single carbon atom.

For 12.011 gram, it takes (12.011 gram × 1 carbon atom / 1.992646547 × 10⁻²³ gram) = 6.0221 × 10²³  $\simeq$ 6.022 × 10²³ carbon atoms (upto 3 sig figs) .

• 6.022 × 10²³ carbon atoms it takes to equal 12.011 grams.

3) A single phosphorus atom has a mass of 30.973 amu

The mass of a single phosphorus atom in grams = 30.973 amu × (1.660539040 × 10⁻²⁴ gram / 1 amu) = 5.143187568 × 10^-23 grams.

• The mass of a single phosphorus atom in grams = 5.143187568 × 10^-23 grams

4) The number of phosphorus atoms it takes to equal 30.973 grams = (30.973 gram × 1 phosphorus atom / 5.143187568 × 10^-23 gram) = 6.02214  × 10²³  $\simeq$  6.022 × 10²³ phosphorus atoms (upto 3 sig figs) .

• 6.022 × 10²³ phosphorus atom it take to equal 30.973 grams.

5) The mass (in amu) of one atom of aluminum (Al) = 26.98154 amu

6) We have 6.022 x 10²³ atoms of aluminum(Al)

The mass of one atom of aluminum (Al) = 26.98154 amu = 26.98154 amu × (1.660539040 × 10⁻²⁴ gram / 1 amu) = 4.48039 × 10^-23 grams.

The mass of 6.022 x 10²³ atoms of aluminum (Al) = 6.022 x 10²³ atoms of Al × (4.48039 × 10^-23 grams / 1 atom of Al) = 26.980 g

• If we had 6.022 x 1023 atoms of aluminum, then the mass of aluminum (in g) = 26.980 g

7) Molar mass: Molar mass of a compound is defined as the mass of 1 mole of the compound. If we describe the mass in grams then the unit of molar mass will be gram/mole i.e. g.mol^-1. 1 mole compound contains 6.022 x 10²³ atoms and the mass of 6.022 x 10²³ atoms is called the molar mass.

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