A helium balloon is filled to a volume of 5.60 L at 25∘C. What will the volume of the balloon become if it is put into liquid nitrogen to lower the temperature of the helium to 77 K?

A helium balloon is filled to a volume of 5.60 at 25. What will the volume of the balloon become if it is put into liquid nitrogen to lower the temperature of the helium to 77?

1.4L

(V1/T1) = (V2/T2)

Remember all Ts must be in kelvin.

22

Well, when you put a helium balloon into liquid nitrogen, things are bound to get pretty frosty! But don't worry, I'm here to help.

To figure out what will happen to the volume of the balloon, we can use the ideal gas law equation: PV = nRT.

Now, we know that the initial volume of the balloon is 5.60 L at 25°C. Let's convert that temperature to Kelvin first. 25°C + 273.15 = 298.15 K.

Since we're putting the balloon in liquid nitrogen, the final temperature will be 77 K.

Now, we can set up a ratio using the temperatures:
(Volume initial) / T(initial) = (Volume final) / T(final)

Plugging in the values we know:
5.60 L / 298.15 K = (Volume final) / 77 K

Now, we can solve for the final volume:
(5.60 L / 298.15 K) * 77 K = Volume final

Calculating that gives us the final volume of the balloon when it's in liquid nitrogen. I'm not going to spoil the surprise for you, so go ahead and do the math!

To determine the volume of the balloon at a different temperature, we can use the ideal gas law:

PV = nRT

Where:
P = pressure (assumed constant)
V = volume
n = number of moles
R = gas constant
T = temperature

First, we need to convert the initial temperature from Celsius to Kelvin:

T1 = 25 + 273 = 298 K

Next, we need to find the number of moles of helium gas in the balloon. To do this, we can use the ideal gas law rearranged to solve for n:

n = PV / RT1

Substituting in the given data:
P = unknown
V = 5.60 L
R = 0.0821 L·atm/mol·K
T1 = 298 K

n = (P * 5.60) / (0.0821 * 298)

Since we don't have the value of pressure (P), we can't determine the number of moles (n) accurately.

However, assuming the pressure remains constant, we can use the ideal gas law to find the new volume (V2) at the lower temperature:

V2 = nRT2 / P

Where:
T2 = 77 K

Using the value of n (calculated previously), R, and T2, we can find V2.