If 16.5 g of oxygen gas is required to inflate a balloon to a certain Volume at 26.5 degrees Celcius, what mass of oxygen gas is required to inflate the same balloon to the same volume and pressure at 10.0 degrees Celcius?

Question

If 16.5 g of oxygen gas is required to inflate a balloon to a certain Volume at 26.5 degrees Celcius, what mass of oxygen gas is required to inflate the same balloon to the same volume and pressure at 10.0 degrees Celcius?

Answer 1

Note the correct spelling of celsius.

I would do the following although it may be the long way around.
Use PV = nRT. Make up a number for V(say an easy number like 1 L) and solve for P. Then substitute that P and the new T and solve for n = number of moles for the new filling. Then n = grams/molar mass and solve for grams. I think the answer is close to 17 grams but that is approximate.

Answer 2

To solve this question, we can use the ideal gas law, which states:

PV = nRT

Where:
P is the pressure of the gas
V is the volume of the gas
n is the number of moles of gas
R is the ideal gas constant
T is the temperature of the gas in Kelvin

First, let's convert the temperature from Celsius to Kelvin for both temperatures:

26.5 degrees Celsius + 273.15 = 299.65 K
10.0 degrees Celsius + 273.15 = 283.15 K

Now, we can set up an equation using the ideal gas law for both situations:

For the first situation at 26.5 degrees Celsius:
PV = nRT

Let's assume the pressure and volume are the same in both situations, so we can write:

P * V = n₁ * R * T₁

For the second situation at 10.0 degrees Celsius:
P * V = n₂ * R * T₂

We are given that the volume and pressure are the same, so we can set these equations equal to each other:

n₁ * R * T₁ = n₂ * R * T₂

Now we can solve for the ratio of the number of moles of gas:

n₂ / n₁ = (T₁ / T₂)

Substituting the given temperatures and solving for the ratio:

n₂ / n₁ = (299.65 K / 283.15 K)

n₂ / n₁ ≈ 1.058

Since moles are directly proportional to mass, we can conclude that the mass of oxygen gas required to inflate the balloon at 10.0 degrees Celsius will be approximately 1.058 times the mass of oxygen gas required to inflate the balloon at 26.5 degrees Celsius.

Therefore, to find the mass of oxygen gas required at 10.0 degrees Celsius, we can multiply the mass of oxygen gas used at 26.5 degrees Celsius by the ratio we obtained:

Mass at 10.0 degrees Celsius = 16.5 g * 1.058 = 17.329 g

Therefore, approximately 17.329 grams of oxygen gas is required to inflate the same balloon to the same volume and pressure at 10.0 degrees Celsius.