896 mL. of a mixture of CO and CO_2 weigh 1.28 g at NTP. Calculate the volume of CO_2 in the mixture at NTP.

Options

A. 448 ml
B. 672 ml
C. 224 ml
D. 500 ml

Answer

To solve the problem of finding the volume of CO₂ in a mixture of CO and CO₂ weighing 1.28 g at NTP, we can follow these steps:

### Step 1: Understand the Given Information
We have:
- Total volume of the mixture (V_total) = 896 mL
- Total weight of the mixture (W_total) = 1.28 g

### Step 2: Define Variables
Let:
- Weight of CO in the mixture = X grams
- Weight of CO₂ in the mixture = (1.28 - X) grams

### Step 3: Calculate Molar Masses
- Molar mass of CO = 12 (C) + 16 (O) = 28 g/mol
- Molar mass of CO₂ = 12 (C) + 2 × 16 (O) = 44 g/mol

### Step 4: Calculate Moles of Each Gas
- Moles of CO = Weight of CO / Molar mass of CO = X / 28
- Moles of CO₂ = Weight of CO₂ / Molar mass of CO₂ = (1.28 - X) / 44

### Step 5: Calculate Total Moles of the Mixture
Using the ideal gas law, we know that 1 mole of gas occupies 22,400 mL at NTP. Therefore, the total moles of the mixture can be calculated from the total volume:
\[ \text{Total moles} = \frac{\text{Volume}}{22400} = \frac{896}{22400} = 0.04 \text{ moles} \]

### Step 6: Set Up the Equation
The total moles of the mixture is the sum of the moles of CO and CO₂:
\[ \frac{X}{28} + \frac{1.28 - X}{44} = 0.04 \]

### Step 7: Solve the Equation
To solve for X, we can multiply through by the least common multiple (LCM) of 28 and 44, which is 616:
\[ 616 \left( \frac{X}{28} \right) + 616 \left( \frac{1.28 - X}{44} \right) = 616 \times 0.04 \]
This simplifies to:
\[ 22X + 14(1.28 - X) = 24.64 \]
Expanding and rearranging gives:
\[ 22X + 17.92 - 14X = 24.64 \]
\[ 8X = 24.64 - 17.92 \]
\[ 8X = 6.72 \]
\[ X = \frac{6.72}{8} = 0.84 \text{ g} \]

### Step 8: Calculate Weight of CO₂
Now, we can find the weight of CO₂:
\[ \text{Weight of CO₂} = 1.28 - X = 1.28 - 0.84 = 0.44 \text{ g} \]

### Step 9: Calculate Moles of CO₂
Now we can find the moles of CO₂:
\[ \text{Moles of CO₂} = \frac{0.44}{44} = 0.01 \text{ moles} \]

### Step 10: Calculate Volume of CO₂
Finally, we can find the volume of CO₂:
\[ \text{Volume of CO₂} = \text{Moles of CO₂} \times 22400 = 0.01 \times 22400 = 224 \text{ mL} \]

### Conclusion
The volume of CO₂ in the mixture at NTP is **224 mL**.

---