Question

A metal, M , of atomic mass 56 amu reacts with chlorine to form a salt that can be represented as MClx. A boiling point elevation experiment is performed to determine the subscript , and therefore, the formula of the salt. A 30.2 g sample of the salt is dissolved in 100.0 g of water and the boiling point of the solution is found to be 376.81 K. Find the formula of the salt. Assume complete dissociation of the salt in solution.
CAN SOMEONE PLEASE HELP ME!!! I AM VERY CONFUSED AND ITS DUE TODAY BEFORE 11:55 THANK YOU IN ADVANCED

Answer 1

Answer:

  MCl₂

Explanation:

The formula for boiling point elevation can be used to find x. The "complete dissociation" means there will be an ion of M and x ions of Cl in the solution. The number of moles of solute will be 30.2 grams divided by the molecular weight of MClx, where x is the variable we're trying to find.

  $\Delta T=imK_b\qquad\text{where i=ions/mole, m=molality, K_b\approx 0.512 }\\\\376.81-373.15=(x+1)\dfrac{\text{moles}}{\text{kg solvent}}(0.512)\\\\\dfrac{3.66}{0.512}=(x+1)\dfrac{\dfrac{30.2}{56+35.45x}}{0.1}=\dfrac{302(x+1)}{56+35.45x}\\\\\dfrac{3.66}{0.512\cdot 302}(56+35.45x)=x+1\\\\\dfrac{3.66\cdot 56}{0.512\cdot 302}-1=x\left(1-\dfrac{3.66\cdot 35.45}{0.512\cdot 302}\right)\\\\x=\dfrac{50.336}{24.877}\approx 2.023$

Then the formula for the salt is MCl₂.