a volatile liquid was allowed to evaporate in a 43.298g flask that has a total volume of 252 mL.,the temperature of the water bath was 100 celcius at the atmospheric pressure of 776 torr.the mass of the flask and condensed vapor was 44.173g.calculate the molar mass of the liquid.
PV = nRT
Solve for n = number of moles.
Then moles = g/molar mass. Solve for molar mass.
To calculate the molar mass of the liquid, we need to apply the ideal gas law, which relates the amount of substance (n), the pressure (P), the volume (V), and the temperature (T) of a gas:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = amount of substance (in moles)
R = ideal gas constant (0.0821 L•atm/mol•K for this problem)
T = temperature (in Kelvin)
First, let's convert the given temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 100°C + 273.15 = 373.15 K
Next, let's convert the pressure from torr to atmospheres:
P(atm) = P(torr) / 760
P(atm) = 776 torr / 760 = 1.02105 atm
Now we can rearrange the ideal gas law equation to solve for n (the amount of substance):
n = PV / RT
Before we calculate "n," we need to determine the volume of the vapor that evaporated. By subtracting the mass of the empty flask from the mass of the flask and condensed vapor, we can obtain the mass of the vapor:
Mass of vapor = Mass of flask and condensed vapor - Mass of empty flask
Mass of vapor = 44.173 g - 43.298 g = 0.875 g
Next, we can calculate the volume of the vapor using its density:
Density = Mass / Volume
Volume = Mass / Density
Since density is mass per unit volume, we can use the total volume of the flask.
Volume = Mass / Total volume = 0.875 g / 252 mL
Note: It's essential to convert the volume from milliliters (mL) to liters (L) for consistency with the ideal gas law.
Volume = (0.875 g * 1 L) / (252 mL * 1000 mL/L) = 0.003472 L
Now we have all the necessary values to calculate the amount of substance, n:
n = (P * V) / (R * T)
n = (1.02105 atm * 0.003472 L) / (0.0821 L·atm/mol·K * 373.15 K)
Calculating this expression will give us the amount of substance in moles. Finally, to find the molar mass (M) of the liquid, we can divide the mass of the liquid by the amount of substance:
Molar mass (M) = Mass / Amount of substance (n)
By following these steps and performing the calculations in this problem, you will be able to determine the molar mass of the liquid.