Respuesta :
Answer: The mass of PVB required to produce 1000 grams of tape is 213.4 grams
Explanation:
To calculate the mass of aluminium oxide, we use the equation:
[tex]\text{Density of substance}=\frac{\text{Mass of substance}}{\text{Volume of substance}}[/tex] .......(1)
- For [tex]Al_2O_3[/tex]
We are given:
50% (v/v) of [tex]Al_2O_3[/tex]
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 = [tex]3.98 g/cm^3[/tex]
Volume of aluminium oxide = [tex]50mL=50cm^3[/tex] (Conversion factor: [tex]1mL=1cm^3[/tex] )
Putting values in equation 1, we get:
[tex]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[/tex]
Mass of aluminium oxide = 199 g
- For PVB:
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 = [tex]1.08 g/cm^3[/tex]
Volume of PVB = [tex]50mL=50cm^3[/tex]
Putting values in equation 1, we get:
[tex]1.08g/cm^3=\frac{\text{Mass of PVB}}{50cm^3}\\\\\text{Mass of PVB}=(1.08g/cm^3\times 50cm^3)=54g[/tex]
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 = [tex]\frac{54}{253}\times 1000=213.4g[/tex]
Hence, the mass of PVB required to produce 1000 grams of tape is 213.4 grams
