# A solution of 2.50 g of a compound having the empirical formula #C_6H_5P# in 25.0 g of benzene is observed to freeze at 4.3°C . What is the molar mass of the solute and its molecular formula?

Here's what I got.

The idea here is that you need to use the *freezing-point depression* equation to determine what the molality of the solution.

Once you have the solution's molality, use it to find the number of moles of solute it contains.

As you know, the equation for *freezing-point depression* looks like this

#color(blue)(DeltaT_f = i * K_f * b)" "# , where

#DeltaT_f# - the freezing-point depression;

#i# - thevan't Hoff factor

#K_f# - thecryoscopic constantof the solvent;

#b# - the molality of the solution.The cryoscopic constant of benzene is equal to

#5.12 ""^@"C kg mol"^(-1)# https://tutor.hix.ai

You're dealing with a non-electrolyte, which means that the van't Hoff factor will be equal to

#1# .The freezing-point depression is defined as

#color(blue)(DeltaT_f = T_f^@ - T_f)" "# , where

#T_f^@# - the freezing point of thepure solvent

#T_f# - the freezing point of the solution

Pure benzenefreezes at#5.5^@"C"# , which means that the freezing-point depression will be

#DeltaT_f = 5.5^@"C" - 4.3^@"C" = 1.2^@"C"# Plug in your values and solve for

#b# , the molality of the solution

#DeltaT_f = i * K_f * b implies b = (DeltaT_f)/(i * K_f)#

#b = (1.2 color(red)(cancel(color(black)(""^@"C"))))/(1 * 5.12 color(red)(cancel(color(black)(""^@"C"))) "kg mol"^(-1)) = "0.2344 mol kg"^(-1)# As you know, molality is defined as moles of solute per kilograms of solvent.

#color(blue)(b = n_"solute"/m_"solvent")# In your case, you have a mass of

#"25.0 g"# of benzene, which means that the solution will contain

#b = n_"solute"/m_"solvent" implies n_"solute" = b xx m_"solvent"#

#n_"solute" = "0.2344 mol" color(red)(cancel(color(black)("kg"^(-1)))) * 25.0 * 10^(-3)color(red)(cancel(color(black)("kg")))#

#n_"solute" = "0.00586 moles"# Now, molar mass is defined as the mass of one mole of a substance. In your case, the

#"2.50-g"# of solute contain a total of#"0.00586"# moles, which means that the molar mass will be

#M_M = "2.50 g"/"0.00586 moles" = "426.6 g/mol"# As you know, a compound's

empirical formulatells you what the smallest whole number ratio that exists between the elements that make up said compound is.The molecular formula, which tells you exactly how many atoms of each element are needed to form the compound, will always be a

multipleof the empirical formula.In this case, calculate the molar mass of the empirical formula by adding the molar masses of all of its constituent elements

#6 xx "12.011 g/mol" + 5 xx "1.00794 g/mol" + 1 xx "30.974 g/mol" = "108.08 g/mol"# You can thus say that

#108.08 color(red)(cancel(color(black)("g/mol"))) * color(blue)(n) = 426.6color(red)(cancel(color(black)("g/mol")))# This will get you

#color(blue)(n) = 426.6/108.08 = 3.95 ~~ 4# The compound's molecular formula will be

#("C"_6"H"_5"P")_color(blue)(4) implies "C"_24"H"_20"P"_4 -># 1, 2, 3, 4 - tetraphenyltetraphosphetane

*Sign up to view the whole answer*

*By signing up, you agree to our Terms of Service and Privacy Policy*

*Sign up with email*

*Answer 2Sign up to view the whole answerSign up with email*

The solute has a molecular formula of C12H10P and a molar mass of about 118.1 g/mol.

By signing up, you agree to our Terms of Service and Privacy Policy

*Answer from HIX Tutor*

*When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.*

*When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.*

*When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.*

*Trending questions*

*What is the mass percent of nitrogen in the dyeing agent, picric acid (#C_6H_3N_3O_7#)?**How many moles of gas occupy 22.4 liters at 27 Celsius degrees and 0.50 atm of pressure?**How do you find the number of molecules or ions of .25 mol #K^+#?**What molar quantity is represented by a #0.46*g# mass of sodium metal?**How many moles are in 50 g of O?*

*Not the question you need?*

*HIX TutorSolve ANY homework problem with a smart AI*

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7