To solve the problem of arranging the given substances in order of increasing mass, we will calculate the mass of each item step by step.
### Step 1: Calculate the mass of one atom of oxygen (O)
- The atomic mass of oxygen (O) is 16 u.
- To find the mass of one atom of oxygen, we use the formula:
\[
\text{Mass of one atom of O} = \frac{\text{Atomic mass of O}}{\text{Avogadro's number}} = \frac{16 \, \text{u}}{6.022 \times 10^{23}} \approx 2.66 \times 10^{-23} \, \text{g}
\]
### Step 2: Calculate the mass of one atom of nitrogen (N)
- The atomic mass of nitrogen (N) is 14 u.
- To find the mass of one atom of nitrogen, we use the same formula:
\[
\text{Mass of one atom of N} = \frac{\text{Atomic mass of N}}{\text{Avogadro's number}} = \frac{14 \, \text{u}}{6.022 \times 10^{23}} \approx 2.32 \times 10^{-23} \, \text{g}
\]
### Step 3: Calculate the mass of \(1 \times 10^{-10}\) moles of oxygen gas (O₂)
- The molar mass of oxygen gas (O₂) is \(32 \, \text{g/mol}\) (since O₂ consists of two oxygen atoms).
- The mass of \(1 \times 10^{-10}\) moles of oxygen gas is calculated as:
\[
\text{Mass of } O_2 = \text{moles} \times \text{molar mass} = 1 \times 10^{-10} \times 32 \, \text{g} = 3.2 \times 10^{-9} \, \text{g}
\]
### Step 4: Calculate the mass of \(1 \times 10^{-10}\) moles of copper (Cu)
- The molar mass of copper (Cu) is \(63 \, \text{g/mol}\).
- The mass of \(1 \times 10^{-10}\) moles of copper is calculated as:
\[
\text{Mass of Cu} = \text{moles} \times \text{molar mass} = 1 \times 10^{-10} \times 63 \, \text{g} = 6.3 \times 10^{-9} \, \text{g}
\]
### Step 5: Compare the masses
Now we have the following masses:
1. Mass of one atom of O: \(2.66 \times 10^{-23} \, \text{g}\)
2. Mass of one atom of N: \(2.32 \times 10^{-23} \, \text{g}\)
3. Mass of \(1 \times 10^{-10}\) moles of O₂: \(3.2 \times 10^{-9} \, \text{g}\)
4. Mass of \(1 \times 10^{-10}\) moles of Cu: \(6.3 \times 10^{-9} \, \text{g}\)
### Step 6: Arrange in increasing order
- \(2.32 \times 10^{-23} \, \text{g}\) (one atom of N)
- \(2.66 \times 10^{-23} \, \text{g}\) (one atom of O)
- \(3.2 \times 10^{-9} \, \text{g}\) (1 x \(10^{-10}\) moles of O₂)
- \(6.3 \times 10^{-9} \, \text{g}\) (1 x \(10^{-10}\) moles of Cu)
### Final Order of Increasing Mass
The order of increasing mass is:
II (one atom of nitrogen) < I (one atom of oxygen) < III (1 x \(10^{-10}\) moles of oxygen gas) < IV (1 x \(10^{-10}\) moles of copper)
