Question

I have an input stream consisting of glycerol, water, and isopropanol, which are equal parts on a volume basis.
What is the composition of the stream on a molar basis?

Answer 1

Answer:

The composition of stream on molar basis for glycerol, water and isopropanol is 16.62%, 67.43% and 15.93% respectively.                

Explanation:

Let suppose the volume is 1 $m^3$. For three equal components volume of each compound is 0.33 $m^3$.

By using the chemical formulas of the compounds, molecular masses are given as

• $mm_g$ is the molecular mass of  glycerol which is 92 g/ mole
• $mm_w$ is the molecular mass of water which is 18 g/mole
• $mm_i$ is the molecular mass of isopropanol which is 60 g/mole

• $\rho_g$ is the density of glycerol which is 1260 $kg/m^3$

• $\rho_w$ is the density of water which is 1000 $kg/m^3$

• $\rho_i$ is the density of isopropanol which is 786 $kg/m^3$

Now using the density and volumes of individual compounds, the masses are given as

                               $V_g=V_w=V_i =0.33 m^3$

Mass of glycerol is

                                       $m_g=\rho_g \times V_g\\m_g=1260 \times 0.33\\m_g=415.8 kg$

Mass of water is

                                    $m_w=\rho_w \times V_w\\m_w=1000 \times 0.33\\m_w=330 kg$

Mass of isopropanol is

                                   $m_i=\rho_i \times V_i\\m_i=786\times 0.33\\m_i=260 kg$

Now number of moles of each compound are given as

Moles of Glycerol are

                                 $n_g=m_g/mm_g\\n_g=415.8 \times 1000/92\\n_g=4519.56 \,moles$

Moles of water are

                                 $n_w=m_w/mm_w\\n_w=330 \times 1000/18\\n_w=18333.33 \,moles$

Moles of isopropanol are

                                 $n_i=m_i/mm_i\\n_i=260 \times 1000/60\\n_i=4333.33 \,moles$

Total number of moles is

                               $n_t=n_g+n_w+n_i\\n_t=27186.22\, moles$

Now composition on molar basis is given as

Molar composition of glycerol is

                               $mn_g= \frac{n_g}{n_t} \times 100\\mn_g= \frac{4519.56}{27186.22} \times 100\\mn_g= 16.62 \%$

Molar composition of water is

                              $mn_w= \frac{n_w}{n_t} \times 100\\mn_w= \frac{18333.33}{27186.22} \times 100\\mn_w= 67.43 \%$

Molar composition of isopropanol is

                             $mn_i= \frac{n_i}{n_t} \times 100\\mn_i= \frac{4333.33}{27186.22} \times 100\\mn_i= 15.93 \%$    

So the composition of stream on molar basis for glycerol, water and isopropanol is 16.62%, 67.43% and 15.93% respectively.