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Sagot :
Solution: (moles of solute)
molarity = moles of solute / volume of solution
moles of solute = molarity × volume of solution
moles of solute = 0.245 mol/L × 0.1500 L
moles of solute = 0.03675 mol
moles of solute = 0.0368 mol
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Solution: (mass of solute)
Step 1: Calculate the molar mass of solute.
molar mass of solute = (40.08 g/mol × 1) + (35.45 g/mol × 2)
molar mass of solute = 110.98 g/mol
Step 2: Calculate the mass of solute.
mass of solute = moles of solute × molar mass of solute
mass of solute = 0.03675 mol × 110.98 g/mol
mass of solute = 4.08 g
Note: The volume of solution must be expressed in liters (L).
Answer:
[tex]\boxed {\sf \bold {0.0368 \ mol \ CaCl_2}}}}[/tex]
[tex]\boxed {\sf \bold {4.08 \ g \ CaCl_2}}}}}[/tex]
Explanation:
1. Moles of Solute
Molarity is a measure of concentration in moles per liter.
[tex]molarity= \frac {moles \ of \ solute}{liters \ of \ solution}[/tex]
In this solution, there are 150.0 milliliters of solution and the molarity is 0.245 M CaCl₂ or 0.245 mol CaCl₂ per liter.
First, convert the milliliters to liters. There are 1000 milliliters in 1 liter.
- [tex]{150 \ mL * \frac{1 \ L}{1000 \ mL}= \frac{150}{1000} \ L = 0.150 \ L[/tex]
Now, substitute the known values (molarity and liters of solution) into the formula. The moles of solution are unknown, so we can use x.
[tex]0.245 \ mol \ CaCl_2 /L= \frac{ x}{0.150 \ L}[/tex]
We are solving for x, so we must isolate this variable. It is being divided by 0.150 L. The inverse of divisions is multiplication, so we multiply both sides by 0.150 L.
[tex]0.150 \ L *0.245 \ mol \ CaCl_2 /L= \frac{ x}{0.150 \ L} * 0.150 L[/tex]
[tex]0.150 \ L *0.245 \ mol \ CaCl_2 /L=x[/tex]
The units of liters cancel.
[tex]0.150 *0.245 \ mol \ CaCl_2 =x[/tex]
[tex]0.03675 \ mol \ CaCl_2[/tex]
The original measurements have 3 significant figures, so our answer must have the same.
We should round to the ten thousandths place. The 5 to the right of this place tells us to round the 7 up to an 8.
[tex]\bold {0.0368 \ mol \ CaCl_2}[/tex]
2. Mass of the Solute
We can convert mass to moles using the molar mass. These values are found on the Periodic Table. They are the same as the atomic masses, but the units are grams per mole (g/mol) instead of atomic mass units.
The solute is calcium chloride: CaCl₂. Look up the molar masses of the individual elements.
- Ca: 40.08 g/mol
- Cl: 35.45 g/mol
Notice that chlorine has a subscript of 2. We must multiply the molar mass by 2.
- Cl₂: 35.45 *2= 70.9 g/mol
Add calcium's molar mass.
- CaCl₂: 40.08 + 70.9 =110.98 g/mol
Use the molar mass as a ratio.
[tex]\frac {110.98 \ g\ CaCL_2}{ 1 \ mol \ CaCl_2}[/tex]
Multiply the moles of calcium chloride we calculated above.
[tex]0.0368 \ mol \ CaCl_2 *\frac {110.98 \ g\ CaCL_2}{ 1 \ mol \ CaCl_2}[/tex]
The units of moles of calcium chloride cancel.
[tex]0.0368 *\frac {110.98 \ g\ CaCL_2}{ 1 }[/tex]
[tex]4.084064 \ g\ CaCl_2[/tex]
Round to 3 significant figures again. For this number, it is the hundredths place. The 4 in the thousandths place tells us to leave the 8.
[tex]\bold {4.08 \ g \ CaCl_2}[/tex]
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