Chloral hydrate \(\left(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{Cl}_{3} \mathrm{O}_{2}\right)\) is a drug formerly used as a sedative and hypnotic. It is the compound used to make "Mickey Finns" in detective stories. a. Calculate the molar mass of chloral hydrate. b. What amount (moles) of \(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{Cl}_{3} \mathrm{O}_{2}\) molecules are in \(500.0 \mathrm{~g}\) chloral hydrate? c. What is the mass in grams of \(2.0 \times 10^{-2}\) mole of chloral hydrate? d. What number of chlorine atoms are in \(5.0 \mathrm{~g}\) chloral hydrate? e. What mass of chloral hydrate would contain \(1.0 \mathrm{~g} \mathrm{Cl}\) ? f. What is the mass of exactly 500 molecules of chloral hydrate?

Step by step solution

01

a. Calculate the molar mass of chloral hydrate.

To calculate the molar mass of chloral hydrate (\(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{Cl}_{3} \mathrm{O}_{2}\)), first find the molar masses of individual elements (from the periodic table): Carbon (C) = 12 g/mol Hydrogen (H) = 1 g/mol Chlorine (Cl) = 35.5 g/mol Oxygen (O) = 16 g/mol Now, using the formula of chloral hydrate, multiply the molar mass of each element with the number of atoms in the compound and sum them up. \(Molar~mass = 2 \times 12 + 3 \times 1 + 3 \times 35.5 + 2 \times 16\)

02

b. Amount (moles) of chloral hydrate in 500.0 g

To find the number of moles of chloral hydrate in 500 g, first, calculate the molar mass of chloral hydrate using the sum from part a. \(Molar~mass = 2 \times 12 + 3 \times 1 + 3 \times 35.5 + 2 \times 16 = 165.5~g/mol\) Now, use the formula for moles: \(moles = \frac{mass}{molar~mass}\) \(moles = \frac{500.0~g}{165.5~g/mol}\)

03

c. Mass of 2.0 x 10^-2 mole of chloral hydrate in grams

To find the mass of this amount of chloral hydrate, use: \(mass = moles \times molar~mass\) \(mass = 2.0 \times 10^{-2}~mol \times 165.5~g/mol\)

04

d. Number of chlorine atoms in 5.0 g chloral hydrate

First, calculate the number of moles of chloral hydrate in 5.0 g: \(moles = \frac{5.0~g}{165.5~g/mol}\) Now, use Avogadro's number to calculate the number of molecules in these moles: \(number~of~molecules = moles \times Avogadro's~number\) Each chloral hydrate molecule consists of 3 chlorine atoms. So, multiply the number of chloral hydrate molecules by 3 to get the total number of chlorine atoms.

05

e. Mass of chloral hydrate containing 1.0 g Cl

First, determine the moles of Cl in 1.0 g: \(moles~of~Cl = \frac{1.0~g}{35.5~g/mol}\) One molecule of chloral hydrate contains 3 Cl atoms. To find the moles of chloral hydrate: \(moles~of~chloral~hydrate = \frac{moles~of~Cl}{3}\) Now, find the mass of these moles of chloral hydrate: \(mass = moles~of~chloral~hydrate \times 165.5~g/mol\)

06

f. Mass of exactly 500 molecules of chloral hydrate

First, convert 500 molecules to moles using Avogadro's number: \(moles = \frac{number~of~molecules}{Avogadro's~number}\) Now, find the mass of these moles of chloral hydrate: \(mass = moles \times 165.5~g/mol\)

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