General Chemistry
General Chemistry
4th Edition
ISBN: 9781891389603
Author: Donald A. McQuarrie, Peter A. Rock, Ethan B. Gallogly
Publisher: University Science Books
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Chapter 13, Problem 13.30P
Interpretation Introduction

Interpretation:

The molecular mass and formula of unknown liquid has to be determined.

Concept Introduction:

The expression to determine molecular weight as per ideal gas equation is given as follows:

  M=mRTPV

Here,

R denotes gas constant.

V denotes the volume.

n denotes the temperature.

P denotes the pressure.

m denotes mass.

M denotes molecular mass.

Expert Solution & Answer
Check Mark

Answer to Problem 13.30P

The molecular mass and formula of unknown liquid is 60.0553 g/mol and C3H8O1  respectively.

Explanation of Solution

The formula to convert degree Celsius to kelvin is as follows:

  T(K)=T(°C)+273 K        (1)

Substitute 10.8 °C for T(°C) in equation (1).

  T(K)=10.8 °C+273 K=283.8 K

The formula to convert cm3 to L is as follows:

  1 cm3=103 L

Thus, 250 cm3 is converted to L as follows:

  Volume=(250 cm3)(103 L1 cm3)=0.25 L

The formula to convert mg to g is as follows:

  1 mg=103 g

Thus, 635 mg is converted to g as follows:

  Mass=(635 mg)(103 g1 kg)=0.635 g

The expression to determine molecular weight as per ideal gas equation is given as follows:

  M=mRTPV        (2)

Substitute 0.635 g for m, 0.25 L for V, 0.998 bar for P, and 0.083145 Lbar/molK for R, 283.8 K for T in equation (2).

  M=(0.635 g)(0.083145 Lbar/molK)(283.8 K)(0.998 bar)(0.25 L)=60.0553 g/mol

Molecular mass of the liquid is 60.0553 g/mol.

The formula to convert mass in grams to moles is as follows:

  Number of moles=Given massmolar mass        (3)

Substitute 2.637 g for mass and 44.01 g/mol for molar mass of CO2 in equation (3) to calculate moles of CO2.

  Moles  of CO2=2.637 g44.01 g/mol=0.059918 mol

Substitute 1.439 g for mass and 18.0152 g/mol for molar mass of H2O  in equation (3) to calculate the moles of H2O.

  Moles  of H2O=1.439 g18.0152 g/mol=0.07987 mol

Substitute 1.200 g for mass of liquid and 60.0553 g/mol for molar mass of H2O  in equation (3) to calculate the moles of H2O.

  Moles  of unknown liquid=1.200 g60.0553 g/mol=0.01998 mol

Moles of C in CO2 are calculated as follows:

  Amount of C(mol)=(0.059918 mol)(1 mol C1 mol CO2)=0.059918 mol C

Moles of H in H2O are calculated as follows:

  Amount of H(mol)=(0.07987 mol)(2 mol H1 mol H2O)=0.15974 mol H

The formula to calculate the mass of carbon in the sample is as follows:

  Mass of C=(Moles of C)(12.01 g C1 mol C)        (4)

The formula to calculate the mass of hydrogen in the sample is as follows:

  Mass of H=(Moles of H)(1.008 g H1 mol H)        (5)

Substitute 0.059918 mol for the amount of C in the equation (4).

  Mass of C=(0.059918 mol C)(12.01 g C1 mol C)=0.719615 g C

Substitute 0.15974 mol for the moles of C in the equation (5).

  Mass of H=(0.15974 mol H)(1.008 g H1 mol H)=0.1610179 g H

The formula to calculate mass of O is as follows:

  Mass of O(g)=Mass of sample(g)(Mass of C+Mass of H)        (6)

Substitute 1.200 g for the mass of the sample, 0.719615 g for massof C, and 0.1610179 g in equation (6).

  Mass of O(g)=1.200 g(0.719615 g+0.1610179 g)=0.31936 g

Substitute 0.31936 g for mass and 16.00 g/mol for molar mass of O in equation (3) to calculate moles of O.

  Moles  of O=0.31936 g16.00 g/mol=0.019960 mol

Write moles of CH and O as subscripts to obtain a preliminary formula as follows:

  C0.059918H0.15974 molO0.0199604

The smallest subscript is 0.0199604. So, divide each subscript by 0.019960 as follows:

  C0.0599180.0199604H0.159740.0199604O0.01996040.0199604C3H8O1

The expression to calculate the empirical formula mass of C3H8O1 is as follows:

  Empirical formula mass=[(3)(M of C)+(8)(M of H)+(1)(M of O)]        (7)

Substitute 12.01 g/mol for M of C, 1.008 g/mol for M of H , 16 g/mol for M of O in equation (7).

  Empirical formula mass=(3)(12.01 g/mol)+(8)(1.008 g/mol)+(1)(16 g/mol)=60.094 g/mol

The formula to calculate the whole number multiple is as follows:

  Whole-number multiple=Molar mass of compoundEmpirical formula mass        (8)

Substitute 60.0553 g/mol for the molar mass of the compound and 60.094 g/mol for the empirical formula mass in equation (8).

  Wholenumber multiple=60.0553 g/mol60.094 g/mol=0.9991

The emprical

Multiply the subscripts in C3H8O1 by 1 to obtain molecular formula.

  Molecular formula=(C3(1)H8(1)O1(1))C3H8O1

The compound is benzene and has a molecular formula of C3H8O1.

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Chapter 13 Solutions

General Chemistry

Ch. 13 - Prob. 13.11PCh. 13 - Prob. 13.12PCh. 13 - Prob. 13.13PCh. 13 - Prob. 13.14PCh. 13 - Prob. 13.15PCh. 13 - Prob. 13.16PCh. 13 - Prob. 13.17PCh. 13 - Prob. 13.18PCh. 13 - Prob. 13.19PCh. 13 - Prob. 13.20PCh. 13 - Prob. 13.21PCh. 13 - Prob. 13.22PCh. 13 - Prob. 13.23PCh. 13 - Prob. 13.24PCh. 13 - Prob. 13.25PCh. 13 - Prob. 13.26PCh. 13 - Prob. 13.27PCh. 13 - Prob. 13.28PCh. 13 - Prob. 13.29PCh. 13 - Prob. 13.30PCh. 13 - Prob. 13.31PCh. 13 - Prob. 13.32PCh. 13 - Prob. 13.33PCh. 13 - Prob. 13.34PCh. 13 - Prob. 13.35PCh. 13 - Prob. 13.36PCh. 13 - Prob. 13.37PCh. 13 - Prob. 13.38PCh. 13 - Prob. 13.39PCh. 13 - Prob. 13.40PCh. 13 - Prob. 13.41PCh. 13 - Prob. 13.42PCh. 13 - Prob. 13.43PCh. 13 - Prob. 13.44PCh. 13 - Prob. 13.45PCh. 13 - Prob. 13.46PCh. 13 - Prob. 13.47PCh. 13 - Prob. 13.48PCh. 13 - Prob. 13.49PCh. 13 - Prob. 13.50PCh. 13 - Prob. 13.51PCh. 13 - Prob. 13.52PCh. 13 - Prob. 13.53PCh. 13 - Prob. 13.54PCh. 13 - Prob. 13.55PCh. 13 - Prob. 13.56PCh. 13 - Prob. 13.57PCh. 13 - Prob. 13.58PCh. 13 - Prob. 13.59PCh. 13 - Prob. 13.60PCh. 13 - Prob. 13.61PCh. 13 - Prob. 13.62PCh. 13 - Prob. 13.63PCh. 13 - Prob. 13.64PCh. 13 - Prob. 13.65PCh. 13 - Prob. 13.66PCh. 13 - Prob. 13.67PCh. 13 - Prob. 13.68PCh. 13 - Prob. 13.69PCh. 13 - Prob. 13.70PCh. 13 - Prob. 13.71PCh. 13 - Prob. 13.72PCh. 13 - Prob. 13.73PCh. 13 - Prob. 13.74PCh. 13 - Prob. 13.75PCh. 13 - Prob. 13.76PCh. 13 - Prob. 13.77PCh. 13 - Prob. 13.78PCh. 13 - Prob. 13.79PCh. 13 - Prob. 13.80PCh. 13 - Prob. 13.81PCh. 13 - Prob. 13.82PCh. 13 - Prob. 13.83PCh. 13 - Prob. 13.84PCh. 13 - Prob. 13.85PCh. 13 - Prob. 13.86PCh. 13 - Prob. 13.87PCh. 13 - Prob. 13.88PCh. 13 - Prob. 13.89PCh. 13 - Prob. 13.90PCh. 13 - Prob. 13.91PCh. 13 - Prob. 13.92PCh. 13 - Prob. 13.93PCh. 13 - Prob. 13.94P
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