The hardness of water (hardness count) is usually expressed as parts per million (by mass) of calcium carbonate. What is the molar concentration of calcium ions in a water sample with a hardness count of 175ppm?
Answer:
1.75 × 10⁻³ M
Explanation:
Given:
Hardness = 175 mg CaCO₃/L
or mass of CaCO₃ in 1 L = 175 × 10⁻³ grams
Now,
Molar mass of CaCO₃ = 40 + 12 + ( 3 × 12 ) = 100 grams/mol
The concentration of CaCO₃ = number of moles / volume
or
= (175 × 10⁻³ / 100) / 1
or
= 1.75 × 10⁻³ M
Now,
CaCO₃ ⇒ Ca²⁺ + CO₃²⁻
1.75 × 10⁻³ M 1.75 × 10⁻³ M 1.75 × 10⁻³ M
thus,
the concentration of Ca²⁺ ions in water = 1.75 × 10⁻³ M
PPM
Ah, talking about water hardness. Well, sounds like we've got some numbers to crunch! Now, let's convert that pesky hardness count of 175ppm into molar concentration of calcium ions.
So, first things first, we need to know the molar mass of calcium carbonate, which is 100.09 g/mol.
Now, to calculate the molar concentration of calcium ions, we need to consider that there's only one calcium ion per calcium carbonate molecule. The atomic mass of calcium is 40.08 g/mol.
Since we know that 175ppm is equivalent to 175mg/L, we can set up a ratio using these values:
175 mg/L (of calcium carbonate) = X mg/L (of calcium ions)
Now, let's do the math!
175 mg/L * (40.08 g/mol / 100.09 g/mol) = X mg/L
After multiplying and dividing, we get X ≈ 69.98 mg/L
Voila! The molar concentration of calcium ions in that water sample with a hardness count of 175ppm is approximately 69.98 mg/L.
To find the molar concentration of calcium ions in a water sample with a hardness count of 175 ppm, we need to convert the ppm value to molar concentration.
First, we need to find the molar mass of calcium carbonate (CaCO3). Calcium has an atomic mass of 40.08 g/mol, carbon has an atomic mass of 12.01 g/mol, and oxygen has an atomic mass of 16.00 g/mol. So, the molar mass of CaCO3 is:
Molar mass of CaCO3 = (1 x 40.08 g/mol) + (1 x 12.01 g/mol) + (3 x 16.00 g/mol)
= 100.09 g/mol
Next, we convert the ppm value to mass by dividing it by 1 million:
175 ppm = 175/1,000,000 = 0.000175 mass fraction
To calculate the mass of calcium carbonate in the water sample, we multiply the mass fraction by the mass of the sample. Let's assume a sample mass of 1 liter (1 kg) for simplicity:
Mass of CaCO3 = 0.000175 x 1 kg
= 0.000175 kg
Now, we can calculate the number of moles of calcium carbonate in the sample using the molar mass:
Moles of CaCO3 = (Mass of CaCO3) / (Molar mass of CaCO3)
= 0.000175 kg / 100.09 g/mol
≈ 1.749 x 10^-6 mol
Since each mole of calcium carbonate contains one mole of calcium ions (Ca2+), the molar concentration (in mol/L or M) of calcium ions in the water sample is the same as the number of moles of calcium carbonate:
Molar concentration of calcium ions = 1.749 x 10^-6 mol/L
So, the molar concentration of calcium ions in a water sample with a hardness count of 175 ppm is approximately 1.749 x 10^-6 mol/L.
1 ppm = 1 mg/L; therefore, 175 ppm = 175 mg CaCO3/L.
Convert to grams Ca ions.
Convert to mols Ca
M = mols Ca/L solution.