A diver exhales a bubble with a volume of 250 mL at a pressure of 2.4 atm and a temperature of 15 °C. How many gas particles are in this bubble?
None of these answers are correct
To determine the number of gas particles in the bubble, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of gas particles
R = ideal gas constant (0.0821 L.atm/mol.K)
T = temperature (in Kelvin)
First, we need to convert the given values to the correct units:
Volume = 250 mL = 0.25 L
Pressure = 2.4 atm
Temperature = 15°C = 15 + 273 = 288 K
Now we can substitute the values into the ideal gas law equation:
(2.4 atm) * (0.25 L) = n * (0.0821 L.atm/mol.K) * (288 K)
Simplifying the equation:
0.6 = 23.5872n
To solve for n, divide both sides of the equation by 23.5872:
n = 0.6 / 23.5872
Calculating this value gives us:
n ≈ 0.0255 mol
Finally, we can convert this value to the number of gas particles by multiplying it by Avogadro's number, which is approximately 6.022 x 10^23 particles/mol:
Number of gas particles = (0.0255 mol) * (6.022 x 10^23 particles/mol)
Calculating this value gives us:
Number of gas particles ≈ 1.537 x 10^22 particles
Therefore, there are approximately 1.537 x 10^22 gas particles in the bubble.