Mixture problem 2 - linear equation

[paulmdrdo1]

1. A clay contains 45% silica and 10% water. Determine the percentage of silica in the clay on a dry (water-free) basis. All percentages are by weight.

my answer is 100% silica. because if the clay is water free the clay is 100% silica. is this correct?

2. A coal contains 2.4% water. After drying, the moisture-free residue contains 71.0% carbon.
Determine the percentage of carbon on the “wet basis.” All percentages are by weight.

for this I have no idea. please give me some assistance here. thanks!

 

[Evgeny.Makarov]

1. A clay contains 45% silica and 10% water. Determine the percentage of silica in the clay on a dry (water-free) basis. All percentages are by weight.

my answer is 100% silica. because if the clay is water free the clay is 100% silica. is this correct?

But before drying silica and water constituted only 45% + 10% = 55% of clay. The rest 45% were other substances. Do you think they evaporated during drying?

Suppose wet clay weighs 100 kg. Then silica weighs 45 kg, water weighs 10 kg and other substances also weigh 45 kg. After drying, water evaporates, but silica and other substances remain. What share of the new total volume does silica make up?

2. A coal contains 2.4% water. After drying, the moisture-free residue contains 71.0% carbon.
Determine the percentage of carbon on the “wet basis.” All percentages are by weight.

for this I have no idea. please give me some assistance here. thanks!

Suppose the orginal coal weighs 100 kg. Then water weighs 2.4 kg, so dry matter, including carbon, weighs 97.6 kg. Of that dry matter carbon makes up 71%. Find the mass of carbon and divide by the original mass, i.e., 100 kg.

 

[paulmdrdo1]

the silica would still be 45%. Am I correct?

please I need a quick response for this. thanks!

 

[Evgeny.Makarov]

Suppose wet clay weighs 100 kg. Then silica weighs 45 kg, water weighs 10 kg and other substances also weigh 45 kg. After drying, water evaporates, but silica and other substances remain. What share of the new total volume does silica make up?

the silica would still be 45%. Am I correct?

No. The total mass (sorry, I mistakenly said volume before) after evaporation is: 45 kg silica + 45 kg other substances = 90 kg. Silica makes up 45 / 90 = 0.5 of that new total mass.

 

[CellCoree]

I would like to provide a clear and thorough explanation for both problems.

For the first problem, we need to determine the percentage of silica in the clay on a dry (water-free) basis. This means we need to calculate the percentage of silica in the clay without taking into account the water content. To do this, we can use the following equation:

% silica on dry basis = (% silica in clay - % water in clay) / (100% - % water in clay)

Substituting the values given in the problem, we get:

% silica on dry basis = (45% - 10%) / (100% - 10%) = 35% / 90% = 0.3888 = 38.88%

This means that on a dry basis, the clay contains 38.88% silica.

Now, for the second problem, we need to determine the percentage of carbon on the "wet basis." This means we need to calculate the percentage of carbon in the coal while taking into account the water content. To do this, we can use the following equation:

% carbon on wet basis = (% carbon in residue / % residue in coal) * 100%

Substituting the values given in the problem, we get:

% carbon on wet basis = (71.0% / 97.6%) * 100% = 72.95%

Therefore, on a wet basis, the coal contains 72.95% carbon. This is because the water content is included in the calculation, so the percentage of carbon is lower compared to the moisture-free residue.

I hope this explanation helps you understand the problems better. Always make sure to carefully read and understand the problem before attempting to solve it, and use the appropriate equations and units to get the correct answer.