<u>Answer:</u> The mass of PVB required to produce 1000 grams of tape is 213.4 grams
<u>Explanation:</u>
To calculate the mass of aluminium oxide, we use the equation:
.......(1)
- <u>For
</u>
We are given:
50% (v/v) of ![Al_2O_3](https://tex.z-dn.net/?f=Al_2O_3)
This means that 50 mL of aluminium oxide is present in 100 mL of tape
Calculating the mass of aluminium oxide by using equation 1:
Density of aluminium oxide = ![3.98 g/cm^3](https://tex.z-dn.net/?f=3.98%20g%2Fcm%5E3)
Volume of aluminium oxide =
(Conversion factor:
)
Putting values in equation 1, we get:
![3.98g/cm^3=\frac{\text{Mass of aluminium oxide}}{50cm^3}\\\\\text{Mass of aluminium oxide}=(3.98g/cm^3\times 50cm^3)=199g](https://tex.z-dn.net/?f=3.98g%2Fcm%5E3%3D%5Cfrac%7B%5Ctext%7BMass%20of%20aluminium%20oxide%7D%7D%7B50cm%5E3%7D%5C%5C%5C%5C%5Ctext%7BMass%20of%20aluminium%20oxide%7D%3D%283.98g%2Fcm%5E3%5Ctimes%2050cm%5E3%29%3D199g)
Mass of aluminium oxide = 199 g
We are given:
50% (v/v) of PVB
This means that 50 mL of PVB is present in 100 mL of tape
Calculating the mass of PVB by using equation 1:
Density of PVB = ![1.08 g/cm^3](https://tex.z-dn.net/?f=1.08%20g%2Fcm%5E3)
Volume of PVB = ![50mL=50cm^3](https://tex.z-dn.net/?f=50mL%3D50cm%5E3)
Putting values in equation 1, we get:
![1.08g/cm^3=\frac{\text{Mass of PVB}}{50cm^3}\\\\\text{Mass of PVB}=(1.08g/cm^3\times 50cm^3)=54g](https://tex.z-dn.net/?f=1.08g%2Fcm%5E3%3D%5Cfrac%7B%5Ctext%7BMass%20of%20PVB%7D%7D%7B50cm%5E3%7D%5C%5C%5C%5C%5Ctext%7BMass%20of%20PVB%7D%3D%281.08g%2Fcm%5E3%5Ctimes%2050cm%5E3%29%3D54g)
Mass of PVB = 54 g
Mass of tape = Mass of aluminium oxide + mass of PVB
Mass of tape = [199 + 54] g = 253 g
To calculate the mass of PVB required to produce 1000 g of tape, we use unitary method:
When 253 grams of tape is made, the mass of PVB required is 54 g
So, when 1000 grams of tape is made, the mass of PVB required will be = ![\frac{54}{253}\times 1000=213.4g](https://tex.z-dn.net/?f=%5Cfrac%7B54%7D%7B253%7D%5Ctimes%201000%3D213.4g)
Hence, the mass of PVB required to produce 1000 grams of tape is 213.4 grams