a solution of CH4N2O in water has a vapor pressure of 19.6 torr. at 25C. what is the mole fraction of CH4N2O in this solution? HELP ME

WATER PURE PRESSURE (P0) IS 23.8 TORR

VAPOR PRESSURE IS 19.6 TORR
DON'T KNOW HOW TO SOLVE IT ?

P(SOLUTION)= X (CH4N2O) WATER (PURE PRESSURE)

i need help please

Answered above.

To find the mole fraction of CH4N2O in the solution, you need to use the formula for vapor pressure lowering:

P(solution) = X(CH4N2O) * P(CH4N2O) + X(water) * P(water)

Where:
P(solution) is the vapor pressure of the solution (19.6 torr),
X(CH4N2O) is the mole fraction of CH4N2O in the solution (what we're trying to find),
P(CH4N2O) is the vapor pressure of pure CH4N2O (unknown),
X(water) is the mole fraction of water in the solution (1 - X(CH4N2O)),
P(water) is the vapor pressure of pure water (23.8 torr).

Since we know the pure pressure of water (P(water)) is 23.8 torr, we need to find the vapor pressure of pure CH4N2O (P(CH4N2O)).

To solve for P(CH4N2O), rearrange the equation as:

P(solution) - X(water) * P(water) = X(CH4N2O) * P(CH4N2O)

Now we can substitute the known values:

19.6 torr - (1 - X(CH4N2O)) * 23.8 torr = X(CH4N2O) * P(CH4N2O)

Simplifying the equation:

19.6 torr - 23.8 torr + 23.8 torr * X(CH4N2O) = X(CH4N2O) * P(CH4N2O)

-4.2 torr + 23.8 torr * X(CH4N2O) = X(CH4N2O) * P(CH4N2O)

Now you need to substitute a reasonable value for P(CH4N2O). Typically, the vapor pressure of a solute is lower than the pure vapor pressure, so let's assume P(CH4N2O) = 0 torr.

This gives us:

-4.2 torr + 23.8 torr * X(CH4N2O) = 0

To solve for X(CH4N2O), rearrange the equation:

23.8 torr * X(CH4N2O) = 4.2 torr

X(CH4N2O) = (4.2 torr) / (23.8 torr)

X(CH4N2O) ≈ 0.176

Therefore, the mole fraction of CH4N2O in the solution is approximately 0.176.