Consider a mole of CO2 and a mole of N2O each at STP. Which of the following statements are true? Check all that apply.
~Both gases will have approximately the same density at these conditions.
~When the volume is not held constant, raising the temperature will decrease the density of both samples
~The CO2 sample will contain fewer molecules of gas.
~When the volume is held constant, raising the temperature will increase the density of both samples.
~N2O will have a higher density at these conditions.
~Both samples will occupy the same volume.
To determine which statements are true, let's analyze each option:
1. Both gases will have approximately the same density at these conditions.
To compare the densities at STP (Standard Temperature and Pressure), we need to consider the molar masses of CO2 and N2O. The molar mass of CO2 is approximately 44 g/mol, while the molar mass of N2O is roughly 44 g/mol. Since both molar masses are the same, the gases will have approximately the same density at these conditions. Therefore, the statement is true.
2. When the volume is not held constant, raising the temperature will decrease the density of both samples.
According to the ideal gas law (PV = nRT), when the volume is not constant, increasing the temperature (T) would lead to an increase in pressure (P) if the number of moles (n) and the volume (V) remain constant. Since density is defined as mass per unit volume, an increase in pressure would result in a decrease in density (assuming mass remains the same). Therefore, this statement is true.
3. The CO2 sample will contain fewer molecules of gas.
Since both CO2 and N2O are given to be at STP, each mole of gas will occupy the same volume. Since both samples contain one mole of gas, they will have an equal number of molecules. Therefore, this statement is false.
4. When the volume is held constant, raising the temperature will increase the density of both samples.
When the volume is held constant, the relationship between pressure (P) and temperature (T) is described by the Gay-Lussac's law (P/T = constant). According to this law, when the temperature increases, the pressure also increases. Since density is inversely proportional to pressure (assuming mass remains constant), an increase in pressure would result in an increase in density at constant volume. Therefore, this statement is false.
5. N2O will have a higher density at these conditions.
As mentioned earlier, both CO2 and N2O have the same molar mass. Since molar mass is a determining factor for the density of gases, the densities of CO2 and N2O at STP will be approximately the same. Therefore, this statement is false.
6. Both samples will occupy the same volume.
Since both gases are given to be at STP (Standard Temperature and Pressure), each mole of gas will occupy 22.4 liters of volume. Since each sample contains one mole of gas, both samples will indeed occupy the same volume. Therefore, this statement is true.
Based on the analysis, the true statements are:
- Both gases will have approximately the same density at these conditions.
- When the volume is not held constant, raising the temperature will decrease the density of both samples.
- Both samples will occupy the same volume.
Both gases will have approximately the same density at these conditions.
When the volume is held constant, raising the temperature will increase the density of both samples.