To calculate the mole fraction of dichloromethane (CH2Cl2) dissolved in water, we begin by converting the given masses into moles. For dichloromethane, we have 25 grams. The molar mass is calculated by summing the atomic masses of its components: 1 carbon (C) at approximately 12.011 g/mol, 2 hydrogens (H) at about 1.008 g/mol each, and 2 chlorines (Cl) at around 35.453 g/mol each. This gives us:
$$\text{Molar mass of CH}_2\text{Cl}_2 = 12.011 + (2 \times 1.008) + (2 \times 35.453) = 84.926 \text{ g/mol}$$
Next, we convert the mass of dichloromethane to moles:
$$\text{Moles of CH}_2\text{Cl}_2 = \frac{25 \text{ g}}{84.926 \text{ g/mol}} \approx 0.2944 \text{ moles}$$
For water, we have 125 grams. The molar mass of water (H2O) is calculated as follows: 2 hydrogens (1.008 g/mol each) and 1 oxygen (O) at approximately 15.999 g/mol:
$$\text{Molar mass of H}_2\text{O} = (2 \times 1.008) + 15.999 = 18.016 \text{ g/mol}$$
Now, we convert the mass of water to moles:
$$\text{Moles of H}_2\text{O} = \frac{125 \text{ g}}{18.016 \text{ g/mol}} \approx 6.9383 \text{ moles}$$
With both components converted to moles, we can now calculate the mole fraction of dichloromethane. The mole fraction (X) is defined as the ratio of the moles of the component of interest to the total moles of all components:
$$X_{\text{CH}_2\text{Cl}_2} = \frac{\text{Moles of CH}_2\text{Cl}_2}{\text{Total moles}}$$
Calculating the total moles:
$$\text{Total moles} = 0.2944 + 6.9383 = 7.2327$$
Now, substituting the values into the mole fraction formula:
$$X_{\text{CH}_2\text{Cl}_2} = \frac{0.2944}{7.2327} \approx 0.04070$$
This result is unitless, as mole fraction is a ratio of moles, and thus cancels out the units. The final answer, with four significant figures, is 0.04070. Remember, the mole fraction is determined by identifying the component of interest and dividing its moles by the total moles of all components involved.