Select the correct answer.
What is the correct mathematical relationship between the number of moles, the volume, and the standard molar volume of a substance?
A. number of moles = volume - standard molar volume
B. number of moles = volume x standard molar volume
C. number of moles = volume / standard molar volume
D. number of moles = standard molar volume / volume
Answer (2)
Define variables: n (number of moles), V (volume), V m (standard molar volume).
State the relationship: The number of moles is the volume divided by the standard molar volume.
Express the formula: n = V m V .
Select the correct option: number of moles = standard molar volume volume
Explanation
Understanding the Problem The question asks us to identify the correct formula that relates the number of moles, the volume, and the standard molar volume of a substance. We need to understand the relationship between these quantities to select the correct option.
Defining Variables and Standard Molar Volume Let's define the variables:
n = number of moles
V = volume
V m = standard molar volume
The standard molar volume ( V m ) is the volume occupied by one mole of a substance under standard conditions (STP). Therefore, the number of moles ( n ) can be found by dividing the total volume ( V ) by the volume occupied by one mole ( V m ).
Establishing the Formula The formula that relates these quantities is:
n = V m V
This means the number of moles is equal to the volume divided by the standard molar volume.
Comparing with the Options Now, let's compare this with the given options:
Option A: number of moles = volume - standard molar volume (Incorrect)
Option B: number of moles = volume x standard molar volume (Incorrect)
Option C: number of moles = standard molar volume volume (Correct)
Option D: number of moles = volume standard molar volume (Incorrect)
Option C matches the formula we derived.
Final Answer Therefore, the correct answer is option C.
number of moles = standard molar volume volume
Examples
In chemistry, understanding the relationship between the number of moles, volume, and standard molar volume is crucial for various calculations. For example, if you have a gas at standard temperature and pressure (STP) and you know its volume, you can determine the number of moles of the gas using the formula: n = V m V , where V m = 22.4 L/mol . This allows you to calculate the mass of the gas or the number of molecules present. This concept is also used in stoichiometry to determine the amount of reactants and products in a chemical reaction.
The correct formula that relates the number of moles, volume, and standard molar volume is n = V m V , indicating that the number of moles is equal to volume divided by standard molar volume. Among the options given, Option C matches this formula. Thus, the correct answer is Option C.
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