A solution contains 0.18 g/mL of a substance X, whose molecular weight is approximately 68000. It is found that 0.27 mL of oxygen at 760 mmHg and `30^@C` will combine with the amount of X contained in 1.0 mL of the solution. How many molecules of oxygen will combine with one molecule of X?

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the moles of oxygen (O2)

We will use the ideal gas law equation:
\[ n = \frac{PV}{RT} \]

Where:
- \( P \) = pressure in atm (760 mmHg)
- \( V \) = volume in liters (0.27 mL = 0.27 × 10^-3 L)
- \( R \) = ideal gas constant (0.0821 L·atm/(K·mol))
- \( T \) = temperature in Kelvin (30°C = 303 K)

**Calculating the pressure in atm:**
\[ P = \frac{760 \text{ mmHg}}{760} = 1 \text{ atm} \]

**Calculating the volume in liters:**
\[ V = 0.27 \text{ mL} = 0.27 \times 10^{-3} \text{ L} \]

**Substituting values into the ideal gas law:**
\[ n = \frac{(1 \text{ atm})(0.27 \times 10^{-3} \text{ L})}{(0.0821 \text{ L·atm/(K·mol)})(303 \text{ K})} \]

Calculating the denominator:
\[ 0.0821 \times 303 \approx 24.9 \]

Now substituting back:
\[ n \approx \frac{0.27 \times 10^{-3}}{24.9} \approx 1.08 \times 10^{-5} \text{ moles of O2} \]

### Step 2: Calculate the mass of substance X in 1 mL of solution

Given that the concentration of substance X is 0.18 g/mL, the mass of X in 1 mL is:
\[ \text{Mass of X} = 0.18 \text{ g} \]

### Step 3: Calculate the moles of substance X

Using the molecular weight of X (68000 g/mol):
\[ \text{Moles of X} = \frac{\text{mass}}{\text{molecular weight}} = \frac{0.18 \text{ g}}{68000 \text{ g/mol}} \]

Calculating:
\[ \text{Moles of X} \approx 2.65 \times 10^{-6} \text{ moles} \]

### Step 4: Determine the ratio of moles of O2 to moles of X

Now, we need to find how many moles of O2 will combine with one mole of X:
\[ \text{Ratio} = \frac{\text{Moles of O2}}{\text{Moles of X}} \]

Substituting the values:
\[ \text{Ratio} = \frac{1.08 \times 10^{-5}}{2.65 \times 10^{-6}} \]

Calculating:
\[ \text{Ratio} \approx 4.07 \]

### Conclusion

This means that approximately 4 molecules of oxygen (O2) will combine with one molecule of substance X.