A small cylinder of helium gas used for filling balloons has a volume of 2.85L and a pressure of 13300kPa at 25 ∘C.How many balloons can you fill if each one has a volume of 1.50L and a pressure of 1.26atm at 25 ∘C?
Well, let's do some balloon math, shall we? Now, first we need to convert the pressure of the cylinder to the same units as the pressure of the balloons.
So, 13300 kPa is approximately equal to (drumroll, please) 13300/101.325 atmospheres. And that gives us 131.31 atmospheres.
Now, let's compare the volumes. We have a cylinder with a volume of 2.85L and balloons with a volume of 1.50L each.
If we divide the volume of the cylinder by the volume of each balloon, we get 2.85/1.50 balloons. That comes out to 1.9 balloons.
So, drumroll again, my friend! With the given numbers, you can fill approximately 1.9 balloons. But since balloons aren't half-inflated (well, unless you're into that sort of thing), let's say you can fill 1 balloon completely and have a second balloon partially filled.
And remember, this is just an estimation! Not all balloons are created equal, and the actual number may vary depending on various factors. But hey, at least now you have an idea of how many balloons you can fill. Happy ballooning!
To solve this problem, we need to use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles of gas
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)
First, let's convert the given pressure and the pressure of the balloons to the same unit.
1 atm = 101.3 kPa
So the pressure of the balloons in kPa is:
1.26 atm × 101.3 kPa/atm = 127.38 kPa
Next, we need to calculate the number of moles of helium gas in the small cylinder.
Using the ideal gas law equation, we can rearrange it to solve for n:
n = PV / RT
Substituting the values into the equation:
n = (13300 kPa × 2.85 L) / (0.0821 L·atm/(mol·K) × (25+273) K)
Simplifying:
n = 3680.5 kPa·L / (21.205 L·kPa/(mol·K) × 298 K)
n = 3680.5 / 6316.99 mol
Now, we can calculate the number of balloons that can be filled using the moles of helium gas and the volume of each balloon:
number of balloons = (number of moles of gas) / (volume of each balloon)
number of balloons = (3680.5 mol) / (1.50 L)
number of balloons ≈ 2453.67
Since we cannot have a fraction of a balloon, we need to round down the number of balloons to a whole number.
Therefore, you can fill approximately 2453 balloons.
To determine how many balloons can be filled, we need to compare the volume and pressure of the helium gas in the cylinder to the volume and pressure required to fill each balloon.
Step 1: Convert the given pressure from kilopascals (kPa) to atmospheres (atm).
1 atm = 101.325 kPa
13300 kPa ÷ 101.325 kPa = 131.46 atm (rounded to two decimal places)
Step 2: Apply the ideal gas law formula to find the moles of helium gas in the cylinder.
The ideal gas law equation is: PV = nRT
where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
We need to find the number of moles (n). Rearranging the equation, we get:
n = PV / RT
n = (131.46 atm) * (2.85 L) / [(0.0821 L·atm/mol·K) * (25 + 273.15 K)]
(Note: we add 273.15 to convert from Celsius to Kelvin)
n ≈ 14.79 moles (rounded to two decimal places)
Step 3: Calculate the number of balloons that can be filled.
To determine the number of balloons, we need to compare the moles of helium gas in the cylinder to the moles required to fill each balloon.
Using the ratio of the moles of helium gas in the cylinder to the moles required for each balloon:
Number of balloons = (Number of moles of helium gas) / (Moles required for each balloon)
Number of balloons = 14.79 moles / [(1.26 atm) * (1.50 L) / [(0.0821 L·atm/mol·K) * (25 + 273.15 K)]]
(Note: we convert the pressure from atm to kPa and add 273.15 to the temperature to convert from Celsius to Kelvin)
Number of balloons ≈ 9.26 balloons (rounded to two decimal places)
Therefore, approximately 9 balloons can be filled using the given cylinder of helium gas.