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Delicious77 [7]
3 years ago
11

A solution of pentane and ethanol (CH3CH2OH)that is 50.% pentane by mass is boiling at 57.2°C. The vapor is collected and cooled

until it condenses to form a new solution.
Calculate the percent by mass of pentane in the new solution. Here's some data you may need:

normal boiling point density vapor pressure at
57.2°C
pentane 36.°C 0.63gmL 1439.torr
ethanol 78.°C 0.79gmL 326.torr
Be sure your answer has 2 significant digits.
dont round during math only for answer!
Note for advanced students: you may assume the solution and vapor above it are ideal.
Chemistry
1 answer:
Paladinen [302]3 years ago
6 0

Answer:

The correct answer is 81.52 percent.

Explanation:

Based on the given information, the boiling point of pentane is 36 degree C and the boiling point of ethanol is 78 degree C. The density of pentane and ethanol is 0.63 g/ml and 0.79 g/ml. The vapor pressure of pentane at 57.2 degree C is 1439 torr and the vapor pressure of ethanol at 57.2 degree C is 326 torr.  

In the given case, 50 percent pentane by mass signifies that mass of pentane is 50 grams. Thus, the mass of ethanol will be 100-50 = 50 grams.  

The moles or n can be calculated by using the formula,  

n = weight/molecular mass

The molecular mass of pentane is 72.15 g per mol and the molar mass of ethanol is 46.07 g/mol.  

The moles of pentane is,  

= 50 g/72.15 g/mol = 0.6930 mol

The moles of ethanol is,  

= 50 g/46.07 g/mol = 1.0853 mol

The mole fraction of pentane is,  

= 0.6930 mol / (0.6930 + 1.0853) mol = 0.3897  

The mole fraction of ethanol is,  

= 1.0853 mol / (0.6930 + 1.0853) mol = 0.6103

Now the vapor pressure of solution will be,  

= pressure of pentane * mole fraction of pentane + pressure of ethanol * mole fraction of ethanol

= (1439 * 0.3897) + (326 * 0.6103)

= 759.736 torr

The vapor pressure of pentane within the solution,  

= vapor pressure of pentane * mole fraction of pentane

= 1439 torr * 0.3897

= 560.778 torr

The fraction of pentane is,  

= 560.778 / 759.736 = 0.738

Let us assume that the total mole is 1, the mole fraction of pentane is 0.738, so the mole fraction of ethanol will become, 1-0.738 = 0.262

The mass of pentane = 0.738 * 72.15 = 53.2467

The mass of ethanol = 0.262 * 46.07 = 12.07034

The percent by mass of pentane in new solution will be,  

Mass% = mass of pentane/Total mass * 100%

= 53.2467/(53.2467 + 12.07034) * 100%

= 53.2467/65.31704 * 100 %

= 81.52 %

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<u>Answer:</u> Nitric oxide is the limiting reagent. The number of moles of excess reagent left is 0.0039 moles. The amount of nitrogen dioxide produced will be 0.7912 g.

<u>Explanation:</u>

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\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}   ....(1)

  • <u>For ozone:</u>

Given mass of ozone = 0.827 g

Molar mass of ozone = 48 g/mol

Putting values in above equation, we get:

\text{Moles of ozone}=\frac{0.827g}{48g/mol}=0.0172mol

  • <u>For nitric oxide:</u>

Given mass of nitric oxide = 0.635 g

Molar mass of nitric oxide = 30.01 g/mol

Putting values in above equation, we get:

\text{Moles of nitric oxide}=\frac{0.635g}{30.01g/mol}=0.0211mol

For the given chemical equation:

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By Stoichiometry of the reaction:

1 mole of ozone reacts with 1 mole of nitric oxide.

So, 0.0172 moles of ozone will react with = \frac{1}{1}\times 0.0172=0.0172moles of nitric oxide

As, given amount of nitric oxide is more than the required amount. So, it is considered as an excess reagent.

Thus, ozone is considered as a limiting reagent because it limits the formation of product.

  • Amount of excess reagent (nitric oxide) left = 0.0211 - 0.0172 = 0.0039 moles

By Stoichiometry of the reaction:

1 mole of ozone produces 1 mole of nitrogen dioxide.

So, 0.0172 moles of ozone will react with = \frac{1}{1}\times 0.0172=0.0172moles of nitrogen dioxide

Now, calculating the mass of nitrogen dioxide from equation 1, we get:

Molar mass of nitrogen dioxide = 46 g/mol

Moles of nitrogen dioxide = 0.0172 moles

Putting values in equation 1, we get:

0.0172mol=\frac{\text{Mass of nitrogen dioxide}}{46g/mol}\\\\\text{Mass of nitrogen dioxide}=0.7912g

Hence, nitric oxide is the limiting reagent. The number of moles of excess reagent left is 0.0039 moles. The amount of nitrogen dioxide produced will be 0.7912 g.

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