Question

For an ideal gas, classify the following pairs of properties as directly or inversely proportional.
P and T
V and n
T and V
P and V
P and n

Answer 1

For an ideal gas, the ideal gas equation can be used to relate the changes in the conditions of the system. The equation is expressed as:

PV = nRT

Therefore, the following are classified as:
P and T = directly proportional
V and n = directly proportional
T and V = directly proportional
P and V = inversely proportional
P and n = directly proportional

Answer 2

The following pairs of properties as

• directly proportional :

P and T

V and n

T and V

P and n

• inversely proportional :

P and V

Further explanation

Some of the laws regarding gas, can apply to ideal gas (volume expansion does not occur when the gas is heated), among others

• Boyle's law at constant T, P = 1 / V
• Charles's law, at constant P, V = T
• Avogadro's law, at constant P and T, V = n

So that the three laws can be combined into a single gas equation, the ideal gas equation

In general, the gas equation can be written

$\large{\boxed{\bold{PV=nRT}}}$

where

P = pressure, atm

V = volume, liter

n = number of moles

R = gas constant = 0.082 l.atm / mol K

T = temperature, Kelvin

Proportional Comparisons / Directly proportional are comparisons of two or more numbers where one number increases, the other numbers also increase at the same rate

Can be formulated  

$\displaystyle \frac {x1} {y1} = \frac {x2} {y2}$

Inversely proportional is the comparison of two or more numbers where one number increases, the other number decreases in value

Can be formulated  

$\displaystyle \frac {x1} {y2} = \frac {x2} {y1}$

The following pairs of properties as directly or inversely proportional.(from ideal gas equation)

P and T  : directly proportional

PV=nRT

V and n  : directly proportional

PV=nRT

T and V  : directly proportional

PV=nRT

P and V  : inversely proportional

$\displaystyle \bold{P}=\frac{nRT}{\bold{V}}$

P and n : directly proportional

PV=nRT

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Keywords : ideal gas law, directly proportional, inversely proportional.