10L of hard water required 5.6g of lime for removing hardness. Hence temporary hardness in ppm of cac03
The answer 1000
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To find the temporary hardness in ppm of CaCO3, we need to use the formula:
Temporary hardness (ppm of CaCO3) = (lime used in grams / volume of water in liters) x 1000
Given that 10L of hard water required 5.6g of lime, we can substitute these values into the formula:
Temporary hardness (ppm of CaCO3) = (5.6g / 10L) x 1000
Simplifying the equation:
Temporary hardness (ppm of CaCO3) = (0.56g/L) x 1000
Temporary hardness (ppm of CaCO3) = 560 ppm
Therefore, the temporary hardness in ppm of CaCO3 is 560 ppm.
To solve this problem, we need to understand the concept of ppm (parts per million) and the formula for calculating temporary hardness.
First, let's define temporary hardness. Temporary hardness is caused by the presence of bicarbonate ions (HCO₃⁻) in water, which can be removed by the addition of lime (calcium hydroxide or Ca(OH)₂).
Now, let's break down the steps to solve the problem:
Step 1: Understand the given information:
- Volume of hard water = 10L
- Lime required to remove hardness = 5.6g
Step 2: Convert the lime mass to moles:
To do this, we need to know the molar mass of lime (Ca(OH)₂). The molar mass of Ca(OH)₂ can be calculated by adding up the atomic masses of its elements (Ca = 40.08 g/mol, O = 16.00 g/mol, H = 1.01 g/mol). Thus, the molar mass of lime is 40.08 + (2 * 16.00) + (2 * 1.01) = 74.10 g/mol.
To convert the mass of lime (5.6 g) to moles, divide the mass by the molar mass:
moles of lime = 5.6 g / 74.10 g/mol
Step 3: Calculate the concentration of temporary hardness:
The concentration is given in ppm, which is equivalent to mg/L.
The concentration of temporary hardness can be calculated using the following formula:
Concentration (ppm) = (moles of lime / volume of water) * molar mass of CaCO₃ * 1000
The molar mass of CaCO₃ is 40.08 + 12.01 + (3 * 16.00) = 100.09 g/mol.
Substituting the values into the formula:
Concentration (ppm) = (moles of lime / 10L) * 100.09 g/mol * 1000
Step 4: Calculate the temporary hardness concentration:
Substitute the value of moles of lime calculated in Step 2:
Concentration (ppm) = (moles of lime / 10L) * 100.09 g/mol * 1000
Step 5: Simplify and compute the final result:
Calculate the concentration using the given values:
Concentration (ppm) = (5.6 g / 74.10 g/mol) / 10L * 100.09 g/mol * 1000
By performing the calculations, you will find that the temporary hardness concentration is 1000 ppm (parts per million) of CaCO₃.
Therefore, the final answer is 1000 ppm.