If the pressure, volume, and the number of moles of a gas are known, which is needed to calculate the universal gas constant from the ideal gas law?
A. the temperature of the gas
B. the molar volume of the gas
C. the molar mass of the gas
D. the partial pressure of the gas
Answer (2)
The ideal gas law is P V = n RT .
To find the universal gas constant R , rearrange the equation to R = n T P V .
Given P , V , and n , the temperature T is needed to calculate R .
Therefore, the answer is the temperature of the gas. the temperature of the gas
Explanation
Understanding the Problem We are asked to determine what variable is needed to calculate the universal gas constant (R) from the ideal gas law, given that pressure (P), volume (V), and the number of moles (n) are known.
Stating the Ideal Gas Law The ideal gas law is given by the equation: P V = n RT where:
P is the pressure of the gas,
V is the volume of the gas,
n is the number of moles of the gas,
R is the universal gas constant,
T is the temperature of the gas.
Solving for R We want to solve for R. To do this, we can rearrange the ideal gas law equation: R = n T P V We are given that P, V, and n are known. Therefore, to calculate R, we need to know the temperature T.
Identifying the Needed Variable The question asks which of the given options is needed to calculate R. From our rearranged equation, it is clear that we need the temperature of the gas.
Final Answer Therefore, the correct answer is the temperature of the gas.
Examples
The ideal gas law is a fundamental concept in chemistry and physics. For example, if you're designing a container to hold a specific amount of gas, you need to know the pressure, volume, and temperature the container will experience. Using the ideal gas law, you can calculate the required volume or pressure, ensuring the container can safely hold the gas. This is crucial in industries like manufacturing, where gases are stored and used in various processes, and in environmental science, where understanding gas behavior helps predict atmospheric changes.
To calculate the universal gas constant (R) from the ideal gas law, we need the temperature of the gas. This is because, in the rearranged equation R = n T P V , the temperature is the only unknown when pressure, volume, and moles are known. Therefore, the correct answer is A. the temperature of the gas.
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