Three balloons filled with three diffferent gaseous compounds each have a volume of 22.4 L at STP. Would these balloons have the same mass or contain the same number of molecules? Explain.
22.4 L of any gas at STP is a mol of the gas. All will contain the same number of molecules since that is 1 mol of molecules; however, they will not have the same mass because different gases have different molar masses.
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To determine whether the balloons have the same mass or contain the same number of molecules, we first need to understand the concept of STP (Standard Temperature and Pressure). STP is defined as a temperature of 273.15 Kelvin (0 °C) and a pressure of 1 atmosphere (101.325 kPa).
Given that the balloons are filled with three different gaseous compounds, we know that each compound will have its own molar mass. The molar mass is the mass of one mole of a substance and is expressed in grams per mole (g/mol).
To compare the mass of the gases in the balloons, we can use the ideal gas law, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
Since the balloons are at STP (standard temperature and pressure), we can replace P with 1 atmosphere and T with 273.15 Kelvin.
PV = nRT
(1 atm)(22.4 L) = n(0.0821 L.atm/mol.K)(273.15 K)
Simplifying the equation, we get:
22.4 atm.L = n(22.4 L.atm/mol)
The 22.4 L on both sides of the equation cancels out, leaving us with:
1 atm = n mol
This equation tells us that at STP, one mole of any gas occupies a volume of 22.4 L. Therefore, regardless of the molar mass or the type of gas, the balloons will contain the same number of moles or molecules.
However, the mass of the balloons will not be the same since the molar mass of each gas will be different. Different gases will have different masses for the same volume at STP.
In summary, the balloons will contain the same number of molecules but will have different masses due to the molar mass of the gases.