Problem 36 - Chemistry The Central Science

Question

(a) What is the mass, in grams, of \(1.223 \mathrm{~mol}\) of iron(III) sulfate? (b) How many moles of ammonium ions are in \(6.955 \mathrm{~g}\) of ammonium carbonate? (c) What is the mass, in grams, of \(1.50 \times 10^{21}\) molecules of aspirin, \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4} ?\) (d) What is the molar mass of diazepam (Valium \(^{\circ}\) ) if 0.05570 mol has a mass of \(15.86 \mathrm{~g}\) ?

Step-by-Step Solution

Answer

(a) The mass of $1.223\, \text{mol}$ of iron(III) sulfate is \(\boldsymbol{399.95 \, \text{g}}\). (b) There are \(\boldsymbol{0.2688\, \text{mol}}\) of ammonium ions in $6.955\, \text{g}$ of ammonium carbonate. (c) The mass of $1.50 \times 10^{21}$ molecules of aspirin is \(\boldsymbol{6.009 \, \text{g}}\). (d) The molar mass of diazepam is \(\boldsymbol{284.8 \, \text{g/mol}}\).

Step 1: Find the molar mass of iron(III) sulfate

To find the mass of iron(III) sulfate, we first need to find its molar mass. Iron(III) sulfate has the chemical formula Fe2(SO4)3. It consists of two Fe atoms, three SO4 units, totaling nine O atoms and three S atoms. To calculate the molar mass of Iron(III) sulfate, multiply the number of atoms of each element by their atomic weights and sum them: \(Molar \, mass = 2 \times (molar \, mass \, of \, Fe) + 3 \times [4 \times (molar \, mass \, of \, O) + (molar \, mass \, of \, S)]\)

Step 2: Calculate the mass of iron(III) sulfate

To calculate the mass of iron(III) sulfate, multiply the given moles by its molar mass: \( Mass = Moles \times Molar \, mass \) #Problem (b)#

Step 3: Obtain the molar mass of ammonium carbonate and calculate moles

Ammonium carbonate has the formula (NH4)2CO3. To calculate the required moles of ammonium ions, first, we find the molar mass of ammonium carbonate and then find the moles of the compound: \( Moles = \frac{Mass}{Molar \, mass} \) Finally, we can determine the moles of ammonium ions in the given mass of ammonium carbonate. #Problem (c)#

Step 4: Find the molar mass of aspirin

Aspirin has the chemical formula C9H8O4. To find the molar mass of aspirin, we multiply the number of atoms of each element by their atomic weights and sum them: \( Molar \, mass \, of \, aspirin = 9 \times (molar \, mass \, of \, C) + 8 \times (molar \, mass \, of \, H) + 4 \times (molar \, mass \, of \, O) \)

Step 5: Calculate the number of moles and mass of aspirin

First, we need to determine the number of moles to calculate the mass of aspirin: \( Number \, of \, moles = \frac{Number \, of \, particles}{Avogadro's \, number}\) Once we have the number of moles, we can find the mass of aspirin using the following formula: \( Mass = Moles \times Molar \, mass \) #Problem (d)#

Step 6: Calculate the molar mass of diazepam

For diazepam, we are given the mass and the number of moles. We can simply find the molar mass using the formula: \( Molar \, mass = \frac{Mass}{Moles} \)