Equal volumes of oxygen gas and a second gas weigh 1.00 and 2.375 grams respectively under the same experimental conditions. Which of the following is the unknown gas?

Options

A. NO
B. `SO_(2)`
C. `CS_(2)`
D. CO

Explanation

To solve the problem of identifying the unknown gas based on the given weights of equal volumes of oxygen and the second gas, we can follow these steps:

### Step 1: Understand the relationship between mass, moles, and molecular weight.
Since the gases are at the same temperature and pressure, we can use the ideal gas law, which implies that equal volumes of gases contain equal numbers of moles under the same conditions.

### Step 2: Set up the equation for moles.
Let \( n_1 \) be the number of moles of oxygen and \( n_2 \) be the number of moles of the unknown gas. Since the volumes are equal, we have:
\[ n_1 = n_2 \]

### Step 3: Calculate the number of moles of oxygen.
The number of moles can be calculated using the formula:
\[ n = \frac{m}{M} \]
where \( m \) is the mass of the gas and \( M \) is the molecular weight of the gas.

For oxygen:
- Mass \( m_1 = 1.00 \, \text{g} \)
- Molecular weight \( M_1 = 32 \, \text{g/mol} \)

Calculating the moles of oxygen:
\[ n_1 = \frac{1.00 \, \text{g}}{32 \, \text{g/mol}} = 0.03125 \, \text{mol} \]

### Step 4: Set up the equation for the unknown gas.
For the unknown gas:
- Mass \( m_2 = 2.375 \, \text{g} \)
- Let the molecular weight of the unknown gas be \( M_2 \).

Using the same formula for moles:
\[ n_2 = \frac{2.375 \, \text{g}}{M_2} \]

### Step 5: Set the moles equal to each other.
Since \( n_1 = n_2 \):
\[ 0.03125 \, \text{mol} = \frac{2.375 \, \text{g}}{M_2} \]

### Step 6: Solve for the molecular weight of the unknown gas.
Rearranging the equation gives:
\[ M_2 = \frac{2.375 \, \text{g}}{0.03125 \, \text{mol}} = 76 \, \text{g/mol} \]

### Step 7: Identify the unknown gas based on its molecular weight.
Now we need to find a gas with a molecular weight of 76 g/mol. We can compare this with the molecular weights of the given options:
- Nitrogen monoxide (NO): 30 g/mol
- Sulfur dioxide (SO2): 64 g/mol
- Carbon disulfide (CS2): 76 g/mol
- Carbon monoxide (CO): 28 g/mol

From the options, we see that Carbon disulfide (CS2) has a molecular weight of 76 g/mol.

### Conclusion:
Thus, the unknown gas is **Carbon disulfide (CS2)**.

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