A certain substance X melts at a temperature of −9.9°C . But if a 350.g sample of X is prepared with 31.8g of urea NH22CO dissolved in it, the sample is found to have a melting point of −13.2°C instead. Calculate the molal freezing point depression constant Kf of X.

Kf = 2.18 °C/m

Explanation:

We must apply the colligative property of freezing point depression:

Freezing T° of pure solvent - Freezing T° of solution = Kf . m

Let's determine data.

Freezing T° of pure solvent = -9.9°C

Freezing T° of solution = -13.2°C

ΔT = -9.9°C - (-13.2°C) = 3.3°C

Kf is the unknown

Let's determine m (molality), moles of solute in 1kg of solvent

X is the solvent. We convert the mass from g to kg

350 g . 1kg / 1000 g  = 0.350 kg

We convert the mass of solute (urea) to moles: 31.8 g / 60g/mol = 0.53 moles

Molality = 0.53 mol / 0.350 kg = 1.51 m

We replace data in the main formula: 3.3°C = Kf . 1.51 m

Kf = 3.3°C / 1.51 m = 2.18 °C/m

The molal freezing point depression constant Kf of X is 2.185 °C / m

Explanation:

Step 1: Data given

Substance X melts at a temperature of −9.9°C

Mass of sample X = 350 grams

Mass of urea = 31.8 grams

Molar mass = 60.06 g/mol

the sample is found to have a melting point of −13.2°C

Step 2: Calculate moles urea

Moles urea = mass urea / molar mass urea

Moles urea = 31.8 grams / 60.06 g/mol

Moles urea = 0.529 moles

Step 3: Calculate molality

Molality = moles urea / mass X

Molality = 0.529 moles / 0.350 kg

Molality = 1.51 molal

Step 4: Calculate the molal freezing point depression constant Kf of X

ΔT =i* Kf * m

⇒with ΔT = the freezing point depression = 3.3 °C

⇒with i = the van't Hoff factor of urea = 1

⇒with Kf = the molal freezing point depression constant Kf of X. = TO BE DETERMINED

⇒with m = the molality = 1.51 molal

3.3 °C = Kf * 1.51 m

Kf = 3.3 °C / 1.51 m

Kf = 2.185 °C / m

The molal freezing point depression constant Kf of X is 2.185 °C / m

most historians agree that gabriel mouton, the vicar of st. paul’s church in lyons, france, is the “founding father” of the metric system. he proposed a decimal system of measurement in 1670. mouton based it on the length of one minute of arc of a great circle of the earth (now called a nautical mile, 1852 meters). he also proposed the swing-length of a pendulum with a frequency of one beat per second as the unit of length (about 25 cm). a pendulum beating with this length would have been fairly easy to produce, thus facilitating the widespread distribution of uniform standards. over the years, his work was revised, improved, and extended by a number of french scientists.

the political sponsor of weights and measures reform in the french revolutionary national assembly was the bishop of autun, better known as talleyrand. under his auspices, the french academy appointed several committees to carry out the work of developing a usable system of weights and measures for france. one of the committees recommended a decimalized measurement system based upon a length equal to one ten-millionth of the length of a quadrant of the earth’s meridian (i.e., one ten-millionth of the distance between the equator and the north pole).