I have a few problems that I am struggling on. I have the answers to all of them

Question

I have a few problems that I am struggling on. I have the answers to all of them, but just don't know how to get to the answer.

1. An RV antifreeze is an aqueous solution containing 5.82 M propylene glycol (MM = 76.09 g/mol). if the density of antifreeze is 1.096 g/mL, what is the molality of the solution?

2. A 16.4 mg sample of a protein was dissolved in water to produce 5.00 mL of solution at 25 degrees C. the osmotic pressure is 1.52 x 10^-3 atm. what is the molar mass of the protein? Note: proteins are nonelectrolytes.

3. The reaction A -> B has rate constant k= .0726 M^-1s^-1. If [A]0= .4000M, how long will it take until [A] = .1200M?

4. The activation energy, Ea, for reaction A->B, to be 21.6 kJ/mol. if the rate constant at 100 degrees C is 2.8x10^-4 s^-1, what is the rate constant at 400 degrees C?

5. A decomposition reaction is first order in A. if the rate constant of the reaction is 2.76 x 10^-2 s^-1, how long will it take for 58% of the material to decompose?

Explanation / Answer

Q1.

Convert:

M = 5.82 mo per liter

MW = 76.09 g/mol

D = 1.096 g/mL

molality = mol of solute / kg of solvent

First, find moles of solute as follows:

Assume a basis of V = 1 Liter of solution

so

M = 5.82 M = 5.82 mol of solute / liter solution

so

mol = 5.82 mol are present

so...

now,

calculate mass of solution

M = D*V

M = 1.096 g/mL * 1 L solution = 1.096 g/mL * 1000 = 1096 g of solution

note that we need kg of solvent, so...

mass of solute = mol*Mw = 5.82*76.09 = 442.8438 g of solute

so..

mass of solvent = mass of solution - mass of solute = 1096-442.8438 = 653.1562 g = 0.6531562 kg of solvent

therefore

Molality = mol of solute / kg solvent = 5.82 / 0.6531562 = 8.910 molal

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