<u>Answer:</u> The mass of the final mixture is 350 grams and composition of methanol in the final mixture is 52.9 %
<u>Explanation:</u>
<u>In first mixture:</u>
Mass of first mixture taken,
= 200 g
Percentage of methanol,
= 40 % = 0.4
Percentage of water,
= (100 - 40)% = 60% = 0.6
<u>In second mixture:</u>
Mass of second mixture,
= 150 g
Percentage of methanol,
= 70 % = 0.7
Percentage of water,
= (100 - 70)% = 30% = 0.3
Let us consider that no chemical reaction is taking place while mixing the solutions.
Calculating the mass of methanol and water in the final mixture:
![m_f=[M_1\chi_m(1)+M_2\chi_m(2)]](https://tex.z-dn.net/?f=m_f%3D%5BM_1%5Cchi_m%281%29%2BM_2%5Cchi_m%282%29%5D)
Putting values in above equation, we get:
![m_f=[(200\times 0.4)+(150\times 0.7)]=185g](https://tex.z-dn.net/?f=m_f%3D%5B%28200%5Ctimes%200.4%29%2B%28150%5Ctimes%200.7%29%5D%3D185g)
![w_f=[M_1\chi_w(1)+M_2\chi_w(2)]](https://tex.z-dn.net/?f=w_f%3D%5BM_1%5Cchi_w%281%29%2BM_2%5Cchi_w%282%29%5D)
Putting values in above equation, we get:
![w_f=[(200\times 0.6)+(150\times 0.3)]=165g](https://tex.z-dn.net/?f=w_f%3D%5B%28200%5Ctimes%200.6%29%2B%28150%5Ctimes%200.3%29%5D%3D165g)
Total mass of the final mixture = ![m_f+w_f=185+165=350g](https://tex.z-dn.net/?f=m_f%2Bw_f%3D185%2B165%3D350g)
To calculate the percentage composition of methanol in final mixture, we use the equation:
![\%\text{ composition of methanol}=\frac{\text{Mass of methanol}}{\text{Mass of final mixture}}\times 100](https://tex.z-dn.net/?f=%5C%25%5Ctext%7B%20composition%20of%20methanol%7D%3D%5Cfrac%7B%5Ctext%7BMass%20of%20methanol%7D%7D%7B%5Ctext%7BMass%20of%20final%20mixture%7D%7D%5Ctimes%20100)
Mass of final mixture = 350 g
Mass of methanol = 185 g
Putting values in above equation, we get:
![\%\text{ composition of methanol in final mixture}=\frac{185g}{350g}\times 100=52.9\%](https://tex.z-dn.net/?f=%5C%25%5Ctext%7B%20composition%20of%20methanol%20in%20final%20mixture%7D%3D%5Cfrac%7B185g%7D%7B350g%7D%5Ctimes%20100%3D52.9%5C%25)
Hence, the mass of the final mixture is 350 grams and composition of methanol in the final mixture is 52.9 %