What is the mass in 3.00 x 10 23 units of calcium chloride, CaCl₂? *
O 1.05 g
O 79.5 g
O 54.8 g
O100 g
54.8 g
To find the mass of calcium chloride, CaCl₂, in 3.00 x 10^23 units, you need to use the molar mass of CaCl₂ and convert the given number of units to grams using Avogadro's constant.
Step 1: Find the molar mass of CaCl₂.
The molar mass of calcium (Ca) is 40.08 g/mol, and the molar mass of chlorine (Cl) is 35.45 g/mol. Since there are two chlorine atoms in CaCl₂, you need to multiply the molar mass of chlorine by 2.
Molar mass of CaCl₂ = (40.08 g/mol) + (2 * 35.45 g/mol) = 111.38 g/mol
Step 2: Convert the given units to moles.
Since Avogadro's constant states that 1 mole of any substance contains 6.022 x 10^23 units, you can use this conversion factor to convert the given units to moles.
Number of moles = (3.00 x 10^23 units) / (6.022 x 10^23 units/mol)
Step 3: Convert moles to grams.
To convert moles to grams, multiply the number of moles by the molar mass of CaCl₂.
Mass in grams = Number of moles * Molar mass of CaCl₂
Now, let's calculate the mass of calcium chloride:
Mass in grams = [(3.00 x 10^23 units) / (6.022 x 10^23 units/mol)] * 111.38 g/mol
Mass in grams = (0.498 mol) * 111.38 g/mol
Mass in grams ≈ 55.52 g
Therefore, the mass of calcium chloride in 3.00 x 10^23 units is approximately 55.52 g.
So, none of the answer options provided exactly matches the calculated mass.
To find the mass of calcium chloride, CaCl₂, in 3.00 x 10 23 units, you need to consider the molar mass of CaCl₂ and the Avogadro's number.
Step 1: Determine the molar mass of CaCl₂.
Calcium (Ca) has an atomic mass of 40.08 g/mol, and chlorine (Cl) has an atomic mass of 35.45 g/mol. Since there are two chlorine atoms in CaCl₂, we need to multiply the atomic mass of chlorine by 2.
Molar mass of CaCl₂ = (1 x atomic mass of Ca) + (2 x atomic mass of Cl)
Molar mass of CaCl₂ = (1 x 40.08 g/mol) + (2 x 35.45 g/mol)
Molar mass of CaCl₂ = 40.08 g/mol + 70.90 g/mol
Molar mass of CaCl₂ = 110.98 g/mol
Step 2: Determine the number of moles of CaCl₂ in 3.00 x 10 23 units.
There are 6.02 x 10^23 units in 1 mole (Avogadro's number).
Number of moles = (Number of units) / (Avogadro's number)
Number of moles = (3.00 x 10^23) / (6.02 x 10^23)
Step 3: Calculate the mass of CaCl₂.
Mass of CaCl₂ = (Number of moles) x (Molar mass of CaCl₂)
Mass of CaCl₂ = [(3.00 x 10^23) / (6.02 x 10^23)] x 110.98 g/mol
Calculating the result:
Mass of CaCl₂ = (3.00 x 10^23) x (110.98 / 6.02 x 10^23) g
Mass of CaCl₂ = 165 g
Therefore, the correct answer is O 165 g.