Question

Chloral hydrate (C2H3Cl3O2) is a drug formerly used as a sedative and hypnotic.
a. Calculate the molar mass of chloral hydrate. b. What amount (moles) of C2H3Cl3O2 molecules are in 500.0 g chloral hydrate? c. What is the mass in grams of 2.0 x 10-2 mol chloral hydrate? d. What number of chlorine atoms are in 5.0 g chloral hydrate? e. What mass of chloral hydrate would contain 1.0 g Cl? f. What is the mass of exactly 500 molecules of chloral hydrate?

Answer 1

Answer :

(a) The molar mass of $C_2H_3Cl_3O_2$ is, 165.5 g/mole

(b) The moles of $C_2H_3Cl_3O_2$ is, 3.02 moles

(c) The mass in grams of $2.0\times 10^{-2}$ mole chloral hydrate is, 3.31 g

(d) The number of chlorine atoms in 5.0 g chloral hydrate is, $5.4\times 10^{22}$

(e) The mass of chloral hydrate will be, 1.55 g

(f) The mass of exactly 500 molecules of chloral hydrate is, $1.99\times 10^{23}$

Explanation :

(a) To calculate the molar mass of chloral hydrate.

The formula of chloral hydrate is, $C_2H_3Cl_3O_2$

Atomic mass of carbon = 12 g/mole

Atomic mass of hydrogen = 1 g/mole

Atomic mass of oxygen = 16 g/mole

Atomic mass of chlorine = 35.5 g/mole

Now we have to determine the molar mass of chloral hydrate.

$\text{Molar mass of }C_2H_3Cl_3O_2$=2(12g/mole)+3(1g/mole)+3(35.5g/mole)+2(16g/mole)=165.5g/mole[/tex]

The molar mass of $C_2H_3Cl_3O_2$ is, 165.5 g/mole

(b) Now we have to determine the moles of $C_2H_3Cl_3O_2$.

$\text{Moles of }C_2H_3Cl_3O_2=\frac{\text{Mass of }C_2H_3Cl_3O_2}{\text{Molar mass of }C_2H_3Cl_3O_2}=\frac{500.0g}{165.5g/mole}=3.02moles$

The moles of $C_2H_3Cl_3O_2$ is, 3.02 moles

(c) Now we have to determine the mass in grams of $2.0\times 10^{-2}$ mole chloral hydrate.

$\text{Mass of }C_2H_3Cl_3O_2=\text{Moles of }C_2H_3Cl_3O_2\times \text{Molar mass of }C_2H_3Cl_3O_2$

$\text{Mass of }C_2H_3Cl_3O_2=(2.0\times 10^{-2}mole)\times (165.5g/mole)=3.31g$

The mass in grams of $2.0\times 10^{-2}$ mole chloral hydrate is, 3.31 g

(d) To calculate the number of chlorine atoms are in 5.0 g chloral hydrate.

First we have to determine the moles of $C_2H_3Cl_3O_2$.

$\text{Moles of }C_2H_3Cl_3O_2=\frac{\text{Mass of }C_2H_3Cl_3O_2}{\text{Molar mass of }C_2H_3Cl_3O_2}=\frac{5g}{165.5g/mole}=0.03moles$

Now we have to calculate the number of chlorine atoms in chloral hydrate.

In $C_2H_3Cl_3O_2$, there are, 2 carbon atoms, 3 hydrogen atoms, 3 chlorine atoms and 2 oxygen atoms.

As, 1 mole of $C_2H_3Cl_3O_2$ contains $3\times 6.022\times 10^{23}$ chlorine atoms

So, 0.03 mole of $C_2H_3Cl_3O_2$ contains $0.03\times 3\times 6.022\times 10^{23}=5.4\times 10^{22}$ chlorine atoms

The number of chlorine atoms in 5.0 g chloral hydrate is, $5.4\times 10^{22}$

(e) To calculate the mass of chloral hydrate would contain 1.0 g Cl.

As, $3\times 35.5g$ of chlorine present in 165.5 g of $C_2H_3Cl_3O_2$

So, 1 g of chlorine present in $\frac{165.5}{3\times 35.5}=1.55g$ of $C_2H_3Cl_3O_2$

The mass of chloral hydrate will be, 1.55 g

(f) To calculate the mass of exactly 500 molecules of chloral hydrate.

As, $6.022\times 10^{23}$ molecules of chloral hydrate has 165.5 g mass of chloral hydrate

So, 500 molecules of chloral hydrate has $\frac{6.022\times 10^{23}}{500}\times 165.5=1.99\times 10^{23}$ mass of chloral hydrate

The mass of exactly 500 molecules of chloral hydrate is, $1.99\times 10^{23}$

Answer 2

The number of molecules of chloral hydrate can be obtained by stoichiometry.

The molar mass of chloral hydrate is the sum of the relative atomic masses of all the elements in the compound. Hence; molar mass of chloral hydrate =

2(12) + 3(1) + 3(35.5) + 2(16) = 24 + 3 + 106.5 + 32 = 165.5 g/mol

Number of moles = mass/molar mass

Mass =  500.0 g

Molar mass = 165.5 g/mol

Number of moles = 500.0 g/ 165.5 g/mol = 3 moles

Mass in grams of 2.0 x 10^-2 moles is obtained from

Number of moles = mass/molar mass

mass = Number of moles × molar mass

mass = 2.0 x 10^-2 moles × 165.5 g/mol

mass = 331 g

Number of moles in 5g of chloral hydrate  = 5g/165.5 g/mol  = 0.03 moles

Number of chlorine atoms in 5g of chloral hydrate = 0.03 moles  × 3  ×6.02  × 10^23 = 5.4 × 10^22

If 165.5 g of chloral hydrate contains 106.5g Cl

x g of chloral hydrate will contain 1 g of Cl

x = 165.5 g ×  1 g/ 106.5

= 1.55 g of  chloral hydrate

1 molecule of chloral hydrate has a mass of 165.5 g

500 molecules of chloral hydrate has a mass of 165.5 g × 500 molecules /1 molecule

= 82750 g

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