Which describes the volume of 1 mol of gas at standard temperature and pressure?
The volume is greater for a larger mass of gas.
The volume is the same for any gas.
The volume depends on the size of the container.
The volume varies with the pressure.
Answer (2)
The volume of 1 mol of gas at standard temperature and pressure (STP) is approximately 22.4 liters, and this volume is the same for any ideal gas. The relationship is dictated by the ideal gas law, where temperature and pressure conditions are constant. Therefore, the correct statement about this volume is that it is the same for any gas.
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The problem asks about the volume of 1 mol of gas at STP.
The ideal gas law, P V = n RT , relates pressure, volume, number of moles, gas constant, and temperature.
At STP, P and T are constant, and n = 1 mol, so V is constant for any gas.
Therefore, the volume is the same for any gas: T h e v o l u m e i s t h es am e f or an y g a s .
Explanation
Understanding the Problem We are asked to identify the correct statement describing the volume of 1 mol of gas at standard temperature and pressure (STP). STP is defined as 0 degrees Celsius (273.15 K) and 1 atmosphere (atm) of pressure. We need to consider the relationship between volume, pressure, temperature, and the number of moles of a gas.
Recalling the Ideal Gas Law The ideal gas law provides the relationship between pressure (P), volume (V), number of moles (n), ideal gas constant (R), and temperature (T):
P V = n RT
Isolating Volume At STP, the temperature T and pressure P are constant. We are given that the number of moles n = 1 mol. The ideal gas constant R is also a constant. Therefore, we can rearrange the ideal gas law to solve for the volume V :
V = P n RT
Calculating the Volume Since n , R , T , and P are all constant at STP for 1 mol of gas, the volume V is also constant. This means the volume is the same for any gas at STP. Let's calculate the volume using R = 0.0821 m o l ⋅ K L ⋅ a t m , T = 273.15 K , P = 1 a t m , and n = 1 m o l :
V = 1 a t m ( 1 m o l ) × ( 0.0821 m o l ⋅ K L ⋅ a t m ) × ( 273.15 K ) = 22.425615 L
Thus, the volume of 1 mol of any ideal gas at STP is approximately 22.4 L.
Determining the Correct Statement Based on the ideal gas law and the calculation, the volume of 1 mol of gas at STP is the same for any gas. The volume does not depend on the size of the container; the gas will expand to fill the container, but the volume of 1 mol at STP is a specific value. The volume does not vary with pressure because the pressure is fixed at STP.
Final Answer Therefore, the correct statement is: The volume is the same for any gas.
Examples
Understanding the volume of gases at STP is crucial in various fields. For instance, in chemistry, it helps in stoichiometric calculations to determine the amount of reactants and products in a chemical reaction. In environmental science, it's used to measure and compare the concentration of different gases in the atmosphere. Moreover, in engineering, knowing the volume of gases at STP is essential for designing and operating systems involving gas storage and transportation. The concept of STP provides a standard reference point for comparing gas volumes, making it easier to analyze and predict gas behavior in different conditions.
