Math  /  Algebra

QuestionFor an ideal gas, which of the following statements is true? a. P is inversely proportional to n at constant V and T . b. P is inversely proportional to T at constant n and V . c. n is inversely proportional to T at constant P and V . d. V is inversely proportional to n at constant P and T . e. V is inversely proportional to T at constant n and P .

Studdy Solution

STEP 1

1. We are dealing with an ideal gas, which follows the ideal gas law.
2. The ideal gas law is given by PV=nRT PV = nRT , where P P is pressure, V V is volume, n n is the number of moles, R R is the ideal gas constant, and T T is temperature.
3. We are analyzing the proportionality of variables while keeping other variables constant.

STEP 2

1. Recall the ideal gas law.
2. Analyze each statement by isolating the variable of interest.
3. Determine the relationship between the variables for each statement.
4. Identify the correct statement based on the ideal gas law.

STEP 3

Recall the ideal gas law:
PV=nRT PV = nRT
This equation relates the pressure P P , volume V V , number of moles n n , and temperature T T of an ideal gas.

STEP 4

Analyze statement (a): "P is inversely proportional to n at constant V and T."
From the ideal gas law:
P=nRTV P = \frac{nRT}{V}
If V V and T T are constant, then P P is directly proportional to n n , not inversely proportional.

STEP 5

Analyze statement (b): "P is inversely proportional to T at constant n and V."
From the ideal gas law:
P=nRTV P = \frac{nRT}{V}
If n n and V V are constant, then P P is directly proportional to T T , not inversely proportional.

STEP 6

Analyze statement (c): "n is inversely proportional to T at constant P and V."
From the ideal gas law:
n=PVRT n = \frac{PV}{RT}
If P P and V V are constant, then n n is inversely proportional to T T .

STEP 7

Analyze statement (d): "V is inversely proportional to n at constant P and T."
From the ideal gas law:
V=nRTP V = \frac{nRT}{P}
If P P and T T are constant, then V V is directly proportional to n n , not inversely proportional.

STEP 8

Analyze statement (e): "V is inversely proportional to T at constant n and P."
From the ideal gas law:
V=nRTP V = \frac{nRT}{P}
If n n and P P are constant, then V V is directly proportional to T T , not inversely proportional.
The correct statement is c \boxed{\text{c}} : "n is inversely proportional to T at constant P and V."

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