The calcium phosphate in a phosphate rock weighing 7.4kg was found to be 477.92mg. What is the concentration of calcium and phosphorous in ppm in the rock sample.
To find the concentration of calcium and phosphorus in parts per million (ppm), we need to determine the amount of calcium and phosphorus in the rock sample, and then convert it to ppm.
First, we need to convert the weight of the phosphate rock from kg to g:
7.4 kg = 7,400 g
Next, we need to convert the amount of calcium phosphate from mg to g:
477.92 mg = 0.47792 g
To find the concentration of calcium in ppm, we can use the following formula:
Concentration (ppm) = (grams of calcium / grams of sample) x 1,000,000
To find the grams of calcium, we need to determine the atomic mass of calcium (Ca) and the calcium-to-calcium phosphate ratio.
The atomic mass of calcium (Ca) is approximately 40.08 g/mol.
The calcium-to-calcium phosphate ratio can be determined by finding the molar mass of calcium phosphate (Ca3(PO4)2) and dividing it by the molar mass of calcium.
The molar mass of calcium phosphate can be calculated as follows:
3(Ca) + 2(P) + 8(O) = (3x40.08) + (2x31.0) + (8x16.00) = 310.18 g/mol
Therefore, the calcium-to-calcium phosphate ratio is:
40.08 g/310.18 g = 0.12919
Now, we can find the grams of calcium by multiplying the calcium-to-calcium phosphate ratio with the grams of calcium phosphate:
0.12919 x 0.47792 g ≈ 0.06178 g
Finally, we can calculate the concentration of calcium in ppm:
Concentration (ppm) = (0.06178 g / 7,400 g) x 1,000,000 = 8.35 ppm
To find the concentration of phosphorus in ppm, we can follow a similar process.
The atomic mass of phosphorus (P) is approximately 31.0 g/mol.
The phosphorus-to-calcium phosphate ratio can be determined by finding the molar mass of calcium phosphate (Ca3(PO4)2) and dividing it by the molar mass of phosphorus.
The molar mass of calcium phosphate can be calculated as mentioned earlier:
3(Ca) + 2(P) + 8(O) = 310.18 g/mol
Therefore, the phosphorus-to-calcium phosphate ratio is:
31.0 g/310.18 g = 0.09994
Now, we can find the grams of phosphorus by multiplying the phosphorus-to-calcium phosphate ratio with the grams of calcium phosphate:
0.09994 x 0.47792 g ≈ 0.04779 g
Finally, we can calculate the concentration of phosphorus in ppm:
Concentration (ppm) = (0.04779 g / 7,400 g) x 1,000,000 = 6.47 ppm
So, the concentration of calcium in the rock sample is approximately 8.35 ppm, and the concentration of phosphorus is approximately 6.47 ppm.