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A small bubble rises from the bottom of a lake, where the temperature and pressure are 4°C and 3.0 atm, to the water's surface, where the temperature is 25°C and the pressure is 0.95 atm. Calculate the final volume of the bubble if its initial volume was 2.1 mL.

Respuesta :

Answer:

7.13mL

Explanation:

P₁V₁T₁ = P₂V₂T₂

P₁ = 3atm , V₁ = 2.1 mL , T₁ = 273 + 4 =277K

P₂ = 0.95atm , V₂ = ? , T₂ = 273 + 25 =298K

V₂ = P₁V₁T₂ / P₂T₁

V₂ = (3atm)(2.1 mL )(298K) / (0.95atm)(277K)

V₂ = 7.13mL

Lanuel

By using the combined gas law, the final volume of the bubble is equal to 41.5 mL.

Given the following data:

  • Initial temperature = 4°C
  • Initial pressure = 3.0 atm.
  • Initial volume = 2.1 mL.
  • Final pressure = 0.95 atm.
  • Final temperature = 25°C

To calculate the final volume of the bubble, we would use the combined gas law:

Mathematically, the combined gas law is given by the formula:

[tex]\frac{PV}{T} = k[/tex]

[tex]\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}[/tex]

Where:

  • P is the pressure of an ideal gas.
  • V is the volume of an ideal gas.
  • is the temperature of an ideal gas.

Making [tex]V_2[/tex] the subject of formula, we have:

[tex]V_2 = \frac{P_1V_1T_2}{P_2T_1}[/tex]

Substituting the given parameters into the formula, we have;

[tex]V_2 = \frac{3 \times 2.1 \times 25}{0.95 \times 4} \\\\V_2 = \frac{157.5}{3.8} \\\\V_2 = 41.5 \; mL[/tex]

Final volume = 41.5 mL

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