Menthol is a crystalline substance with a peppermint taste and odor. when 1.03 g of menthol is dissolved in 25.0 g of cyclohexane, the freezing point of the solution is lowered by 5.49 °c. the freezing point and kf constant for cyclohexane can be found here. calculate the molar mass of menthol.

- molar mass of menthol is 156.06 g/mol.

Solution:- delta Tf = i x m x kf

where, delta Tf is depression in freezing point.

i is Van't hoff factor, m is molality and kf is the molal freezing point constant.

menthol is covalent molecule and so the value of i for this is 1 as it does not give ions.

delta Tf = 5.49 degree C

kf for cyclohexane is 20.8 degree C/m

Let's plug in the values in the formula..

5.49 = 1 x m x 20.8

m = 5.49/20.8

m = 0.264

molality = moles of solute/kg of solvent

There are 25.0 g that is 0.025 kg of solvent.

So, 0.264 = moles of solute/0.025

moles of solute = 0.264(0.025) = 0.0066

moles = mass/molar mass

So, molar mass = mass/moles

molar mass = 1.03 g/0.0066 mol

molar mass = 156.06 g/mol

The molar mass of menthol is  153 g/mol.

Using;

ΔT = K m i

ΔT = Freezing point depression

K = Freezing point depression constant of cyclohexane

m = molality of solution

i = Van't Hoff Factor

5.49 °C = 20.20 °C/m × m × 1 (menthol is molecular)

m = 5.49 °C/20.20 °C/m  = 0.27 m

But;

Molality = Number of moles of solute/Mass of solution in Kg

Mass of solution = 25.0 g  or 0.025 Kg

Number of moles = mass/molar mass

Let the molar mass of menthol be x

Mass of menthol dissolved is 1.03 g

Hence;

0.27 = 1.03/x/ 0.025

0.27 = 1.03/0.025 x

0.27 (0.025 x) = 1.03

0.00675x = 1.03

x = 1.03/0.00675

x = 153 g/mol

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(newtons first law)

conservation of momentum law states :

momentum before collision = momentum after collision

momentum p (kg-m/s)= mass * velocity

say moving car=1 000 kg, velocity = 10 m/s then p = 1 000*10= 10 000 kg-m/s

say still car = 2 000 kg, velocity = 0 m/s then p = 2 000* 0 = 0 kg-m/s

total momentum prior to collision = 10 000 + 0 = 10 000 kg-m/s

momentum after collision = 10 000 kg-m/s

mass now = 1 000 kg+2 000 kg = 3 000 kg

10 000 = 3 000 kg* velocity m/s

10 000/3 000 = velocity

3.33 m/s = velocity after collision

an impulse is a force applied over time , momentum is exclusive of external forces and a perfect collision is implied