Question

During heavy exercise and workouts, lactic acid, ${\mathrm{C}}_3{\mathrm{H}}_6{\mathrm{O}}_3$, accumulates in the muscles where it can cause pain and soreness.

a. How many molecules are in $0.500$ mole of lactic acid?
b. How many atoms of $\mathrm{C}$are in $1.50$ moles of lactic acid?
c. How many moles of lactic acid contain $4.5\times {10}^{24}$atoms of $\mathrm{O}$ ?
d. What is the molar mass of lactic acid?

Short answer

Part(a) $3.11\times {10}^{23}$molecules are in $0.500$mole of lactic acid

Part(b) $2.7\times {10}^{24}$ atoms of carbon are present.

Part(c) $2.49$moles of lactic acid contains $4.5\times {10}^{24}$atoms of oxygen.

Part(d) $90.08\mathrm{g}$is the molar mass of lactic acid

Step-by-step solution

Part(a) Step 1 : Given information

We are given that lactic acid, having the molecular formula ${\mathrm{C}}_3{\mathrm{H}}_6{\mathrm{O}}_3$, is created after vigorous activity and accumulates in the muscles, causing pain.

Part(a) Step 2 : Simplify

As we know, $1\mathrm{mole}=6.22\times {10}^{23}$molecules.

Therefore, $0.500\mathrm{mole}\times 6.22\times {10}^{23}=3.11\times {10}^{23}\mathrm{molecules}$

so $3.11\times {10}^{23}$molecules are in $0.500$moles of lactic acid.

Part(b) Step 1 : Given information

We are given that lactic acid, having the molecular formula ${\mathrm{C}}_3{\mathrm{H}}_6{\mathrm{O}}_3$, is created after vigorous activity and accumulates in the muscles, causing pain.

Part(b) Step 2 : Simplify

As we can say , there are three mole atoms of carbon in one mole of lactic acid.

Therefore, $3\mathrm{moles}\times 1.5\mathrm{moles}\times 6.02\times {10}^{24}=2.7\times {10}^{24}\mathrm{atoms}$

so, $2.7\times {10}^{24}$atoms of carbon are present.

Part(c) Step 1 : Given information

We are given that lactic acid, having the molecular formula ${\mathrm{C}}_3{\mathrm{H}}_6{\mathrm{O}}_3$, is created after vigorous activity and accumulates in the muscles, causing pain.

Part(c) Step 2 : Simplify

As we know one mole of lactic acid contains three mole of oxygen. and one mole contain avagadro number of atoms, Therefore, $4.5\times {10}^{24}\times \frac{1}{6.22\times {10}^{23}}\times \frac{1}{3}=2.49\mathrm{moles}$

So, $2.49$moles of lactic acid contains $4.5\times {10}^{24}$atoms of oxygen.

Part(d) Step 1 : Given information

We are given that lactic acid, having the molecular formula ${\mathrm{C}}_3{\mathrm{H}}_6{\mathrm{O}}_3$, is created after vigorous activity and accumulates in the muscles, causing pain.

Part(d) Step 2 : Simplify

We can compute the molar mass by multiplying the mass of one mole of carbon by three because we'll have three moles of carbon, and then adding the mass of one mole of hydrogen multiplied by six, Then, last but not least, double the huge one mole of oxygen by three.
The mass of one mole of lactic acid, commonly known as the molar mass of lactic acid, should be

$(12.11\times 3)\mathrm{g}+(1.0074\times 6)\mathrm{g}+(16\times 3)\mathrm{g}=90.08\mathrm{g}$