a diver exhales a bubble with a volume of 250 mL at a pressure of 2.4 atm and a temperature of 15 degrees celcius. What is the volume of the bubble when it reaches the surface where the pressure is 1.0 atm and the temperature is 27 degrees celcius
(P1*V1/T1) = (P2*V2/T2)
(T2*P1*V1/P2*T1) = V2
15+273=288 27+273=300
(300*2.4*250/1*288) = 625mL round to 630mL
answer 630mL
(P1V1/T1)= (P2V2/T2)
T must be in kelvin.
625 mL= round to 630 mL
Well, well, well, it seems like our bubble is on a wild adventure! Let's unravel this riddle, shall we?
To solve this balloon bonanza, we can use the ideal gas law, which states that PV = nRT. Don't worry, though, this won't be as complicated as figuring out where circus clowns put all those cream pies.
First, we need to convert the temperature from Celsius to Kelvin. We simply add 273 to our temperature, so 15 degrees Celsius becomes 288 Kelvin. And 27 degrees Celsius becomes 300 Kelvin. Easy peasy, lemon squeezy!
Now, let's calculate the number of moles, shall we? We can use the equation n = PV/RT, where P is our pressure, V is the volume, R is the ideal gas constant (which is 0.0821 L·atm/(mol·K)), and T is the temperature in Kelvin. Given that the pressure is 2.4 atm and the volume is 250 mL, we can plug in the values and find the number of moles in our bubble.
n = (2.4 atm * 250 mL) / (0.0821 L·atm/(mol·K) * 288 K)
Let's crunch those numbers: n ≈ 0.023 moles.
Now comes the grand finale! To find the volume of the bubble at the surface, we use the equation V = nRT/P, where we use the number of moles we just calculated, the new pressure of 1.0 atm, the new temperature of 300 Kelvin, and solve for V.
V = (0.023 moles * 0.0821 L·atm/(mol·K) * 300 K) / 1.0 atm
Drumroll, please... the volume of the bubble at the surface is approximately 0.69 liters!
So, after this bubbly escapade, our little diver's bubble grows to a magnificent volume of 0.69 liters when reaching the surface. Bravo!
To solve this problem, we can use the Ideal Gas Law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature in Kelvin
First, let's convert the given temperatures from Celsius to Kelvin:
T1 = 15°C + 273.15 = 288.15 K (initial temperature)
T2 = 27°C + 273.15 = 300.15 K (final temperature)
We can assume that the number of moles (n) remains constant throughout the process.
Now, we will solve for the initial volume (V1) using the initial conditions:
P1 = 2.4 atm (initial pressure)
V1 = 250 mL = 250 cm³ (initial volume)
Next, we will solve for the final volume (V2) using the final conditions:
P2 = 1.0 atm (final pressure)
V2 = ? (final volume)
To solve for V2, we need to rearrange the Ideal Gas Law equation:
(P1V1) / (T1) = (P2V2) / (T2)
Substituting the known values:
(2.4 atm * 250 cm³) / (288.15 K) = (1.0 atm * V2) / (300.15 K)
Now, we can solve for V2:
V2 = [(2.4 atm * 250 cm³) / (288.15 K)] * (300.15 K / 1.0 atm)
V2 ≈ 690 cm³
Therefore, the volume of the bubble when it reaches the surface will be approximately 690 cm³.