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What is the molarity of an aqueous solution that contains 78g of C6H12O6 dissolved in 2500 mL of solution?

Sagot :

Sarah06109

Answer:

[tex]\boxed {\boxed {\sf molarity = 0.17 \ M \ C_6H_12O_6}}[/tex]

Explanation:

Molarity is found by dividing the moles of solute by liters of solution.

[tex]molarity = \frac {moles}{liters}[/tex]

We are given grams of a compound and milliliters of solution, so we must make 2 conversions.

1. Gram to Moles

We must use the molar mass. First, use the Periodic Table to find the molar masses of the individual elements.

  • C: 12.011 g/mol
  • H: 1.008 g/mol
  • O: 15.999 g/mol

Next, look at the formula and note the subscripts. This tells us the number of atoms in 1 molecule. We multiply the molar mass of each element by its subscript.

6(12.011)+12(1.008)+6(15.999)=180.156 g/mol

Use this number as a ratio.

[tex]\frac {180.156 \ g\ C_6H_12 O_6}{ 1 \ mol \ C_6H_12O_6}[/tex]

Multiply by the given number of grams.

[tex]78 \ g \ C_6H_12O_6 *\frac {180.156 \ g\ C_6H_12 O_6}{ 1 \ mol \ C_6H_12O_6}[/tex]

Flip the fraction and divide.

[tex]78 \ g \ C_6H_12O_6 *\frac { 1 \ mol \ C_6H_12O_6}{180.156 \ g\ C_6H_12 O_6}[/tex]

[tex]\frac { 78 \ mol \ C_6H_12O_6}{180.156 }= 0.432958102977 \ mol \ C_6H_12O_6[/tex]

2. Milliliters to Liters

There are 1000 milliliters in 1 liter.

[tex]\frac {1 \ L }{ 1000 \ mL}[/tex]

Multiply by 2500 mL.

[tex]2500 \ mL* \frac {1 \ L }{ 1000 \ mL}[/tex]

[tex]2500 * \frac {1 \ L }{ 1000 }= 2.5 \ L[/tex]

3. Calculate Molarity

Finally, divide the moles by the liters.

[tex]molarity = \frac {0.432958102977 \ mol \ C_6H_12O_6}{ 2.5 \ L}[/tex]

[tex]molarity = 0.173183241191 \ mol \ C_6H_12O_6/L[/tex]

The original measurement has 2 significant figures, so our answer must have the same. That is the hundredth place and the 3 tells us to leave the 7.

[tex]molarity \approx 0.17 \ mol \ C_6H_12O_6 /L[/tex]

1 mole per liter is also equal to 1 M.

[tex]molarity = 0.17 \ M \ C_6H_12O_6[/tex]

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