A balloon is filled with 4.57 liters of air at room temperature(23.3 deg C). Liquid nitrogen is poured over the balloon until the gas is at a temperature of -197 degrees C. What volume with the gas have inside the balloon?

Question

The pressure on the inside of the balloon will remain constant throughout the experiment

Avery Adams · Accepted Answer

#V_2# = #1.22L#

So refer to the Charle's Law equation

#(V_1)/(T_1)# = #(V_2)/(T_2)#

We have our first volume #(V_1)# which is #4.57 L# Our first temperature #(T_1)# which is #23.3^@C# And our second temperature #(T_2)# which is #-197^@C#

Our unknown is the second volume #(V_2)#

Before we plug our values into the equation, we need to convert the temperature into Kelvin #(K)#

We can do this by taking the #C^@# and adding #273#

#T_1#: #23.3^@C# + #273# = #296.3K#

#T_2#: #-197^@C# + #273# = #76K#

Now we can plug our values into the equation

#(4.57 L)/(296.3K)#=#(V_2)/(76K)#

We need to isolate #V_2# so we multiply both sides by #(76K)/(1)#

#(76cancelK)/(1)# x #(4.57 L)/(296.3cancelK)#=#(V_2)/(cancel(76K))# x #(cancel(76K))/(1)#

After you multiply #76# by #4.57L# then divide by #296.3#, your answer should be

#V_2# = #1.22L#

Wyatt Adkins · Answer

undefined To solve this problem, we can use the ideal gas law equation, 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, and $ T $ is the temperature of the gas in Kelvin.

First, we need to convert the temperatures from Celsius to Kelvin using the equation: $ T(K) = T(C) + 273.15 $.
For the initial temperature, $ T_i = 23.3^\circ C + 273.15 = 296.45 K $.
For the final temperature, $ T_f = -197^\circ C + 273.15 = 76.15 K $.

The initial volume of the balloon is given as 4.57 liters.

Next, we need to find the number of moles of gas using the ideal gas law equation: $ n = \frac{PV}{RT} $.
We'll assume that the pressure remains constant, which is reasonable since the problem doesn't specify any change in pressure.

Given that the balloon is filled with air at room temperature, we can use the molar volume of gas at room temperature and pressure, which is approximately $ 22.4 \, \text{L/mol} $.

So, $ n = \frac{4.57 \, \text{L}}{22.4 \, \text{L/mol}} $.

Now, we can use the ideal gas law to find the final volume of the gas:
$ V_f = \frac{n \cdot R \cdot T_f}{P} $.

Substituting the values, we get:
$ V_f = \frac{\left(\frac{4.57 \, \text{L}}{22.4 \, \text{L/mol}}\right) \cdot R \cdot 76.15 \, \text{K}}{P} $.

Since the pressure is constant and not given, we can't calculate the exact final volume without that information. However, the final volume will be smaller than the initial volume due to the decrease in temperature, according to the ideal gas law.