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Novosadov [1.4K]
3 years ago
12

Three 1.0-l flasks, maintained at 308 k, are connected to each other with stopcocks. initially the stopcocks are closed. one of

the flasks contains 1.5 atm of n2, the second 2.2 g of h2o, and the third, 0.30 g of ethanol, c2h6o. the vapor pressure of h2o at 308 k is 42 mmhg and that of ethanol is 102 mmhg. the stopcocks are then opened and the contents mix freely. what is the pressure
Chemistry
1 answer:
Licemer1 [7]3 years ago
3 0

Answer:

0.6103 atm.

Explanation:

  • We need to calculate the vapor pressure of each component after the stopcocks are opened.
  • Volume after the stopcocks are opened = 3.0 L.

<u><em>1) For N₂:</em></u>

P₁V₁ = P₂V₂

P₁ = 1.5 atm & V₁ = 1.0 L & V₂ = 3.0 L.

P₂ of N₂ = P₁V₁ / V₂ = (1.5 atm) (1.0 L) / (3.0 L) = 0.5 atm.

<u><em>2) For H₂O:</em></u>

Pressure of water at 308 K is 42.0 mmHg.

we need to convert from mmHg to atm: <em>(1.0 atm = 760.0 mmHg)</em>.

P of H₂O = (1.0 atm x 42.0 mmHg) / (760.0 mmHg) = 0.0553 atm.

We must check if more 2.2 g of water is evaporated,

n = PV/RT = (0.0553 atm) (3.0 L) / (0.082 L.atm/mol.K) (308 K) = 0.00656 mole.

m = n x cmolar mass = (0.00656 mole) (18.0 g/mole) = 0.118 g.

It is lower than the mass of water in the flask (2.2 g).

<em><u>3) For C₂H₅OH:</u></em>

Pressure of C₂H₅OH at 308 K is 102.0 mmHg.

we need to convert from mmHg to atm: (1.0 atm = 760.0 mmHg).

P of C₂H₅OH = (1.0 atm x 102.0 mmHg) / (760.0 mmHg) = 0.13421 atm.

We must check if more 0.3 g of C₂H₅OH is evaporated,

n = PV/RT = (0.13421 atm) (3.0 L) / (0.082 L.atm/mol.K) (308 K) = 0.01594 mole.

m = n x molar mass = (0.01594 mole) (46.07 g/mole) = 0.7344 g.

<em>It is more than the amount in the flask (0.3 g), so the pressure should be less than 0.13421 atm.</em>

We have n = mass / molar mass = (0.30 g) / (46.07 g/mole) = 0.00651 mole.

So, P of C₂H₅OH = nRT / V = (0.00651 mole) (0.082 L.atm/mole.K) (308.0 K) / (3.0 L) = 0.055 atm.

  • <em>So, </em><em>total pressure</em><em> = </em><em>P of N₂ + P of H₂O + P of C₂H₅OH</em><em> = 0.5 atm + 0.0553 atm + 0.055 atm = </em><em>0.6103 atm</em><em>.</em>
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<h3>General Formulas and Concepts:</h3>

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<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
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  3. Exponents
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[RxN - Balanced] C₆H₁₂O₆ → 2C₂H₅OH + 2CO₂

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<u>Step 2: Identify Conversions</u>

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Molar Mass of C₆H₁₂O₆ - 6(12.01) + 12(1.01) + 6(16.00) = 180.18 g/mol

<u>Step 3: Stoichiometry</u>

  1. [DA] Set up conversion:                                                                                 \displaystyle 500 \ g \ C_6H_{12}O_6(\frac{1 \ mol \ C_6H_{12}O_6}{180.18 \ g \ C_6H_{12}O_6})(\frac{2 \ mol \ C_2H_5OH}{1 \ mol \ C_6H_{12}O_6})
  2. [DA} Multiply/Divide [Cancel out units]:                                                         \displaystyle 5.55001 \ mol \ C_2H_5OH

<u>Step 4: Check</u>

<em>Follow sig fig rules and round. We are given 3 sig figs.</em>

5.55001 mol C₂H₅OH ≈ 5.55 mol C₂H₅OH

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