Question

Write the units of the gas constant R in different scales of measurement ?

Solution

The units of the gas constant (or numerical value) R in different scales of measurement may be calculated as follows:

1. In SI units:
One mole of a gas under standard conditions of temperature and pressure (STP or NTP) occupies a volume of 22·7L.
$therefore space space space Pressure space left parenthesis straight P right parenthesis space equals space 1 space bar space equals space 10 to the power of 5 Pa Temperature space left parenthesis straight T right parenthesis space equals space 273.15 space straight K Volume space left parenthesis straight V right parenthesis space equals space 22.7 space straight L space space equals space 22.7 space cross times space 10 to the power of negative 3 end exponent straight m cubed According space to space ideal space gas space equation comma space space space space space space space space space PV space equals space nRT or space space space space space space space straight R space equals space PV over nT or space space space space space space space space straight R space equals space fraction numerator 10 to the power of 5 Pa space cross times space 22.7 space cross times space 10 to the power of negative 3 end exponent straight m cubed over denominator 1 space mol space cross times space 273.15 space straight K end fraction space space space space space$
$space equals space fraction numerator 10 to the power of 5 Nm to the power of negative 2 end exponent space cross times space 22.7 space cross times space 10 cubed straight m cubed over denominator 1 space mol space cross times space 273.15 space straight K end fraction space equals space 8.314 space Nm space mol to the power of negative 1 end exponent straight K to the power of negative 1 end exponent space equals space 8.314 space straight J space mol to the power of negative 1 end exponent straight K to the power of negative 1 end exponent left parenthesis 1 space NM space equals space 1 straight J right parenthesis$

2. Under NTP condition (for one mole of the gas):One mole of any gas at 0°C (i.e. 273·15K.) and under 1 bar pressure occupies 22.7 L
$therefore space space space space Pressure space left parenthesis straight P right parenthesis space equals space 1.0 space bar space Temperature space left parenthesis straight T right parenthesis space equals space space 273.15 space straight K Volume space left parenthesis straight V right parenthesis space equals space 22.7 space dm cubed space space space space space space space space space space space space straight n space equals space 1 space mol$
According to ideal gas equation,
PV = nRT
$or space space space space space space space space space straight R space equals space PV over nT$
Substituting the values, we have,
$straight R space equals space fraction numerator left parenthesis 1.0 space bar right parenthesis space cross times space left parenthesis 22.7 space dm cubed right parenthesis over denominator left parenthesis 1 space mol right parenthesis space cross times space left parenthesis 273.15 space straight K right parenthesis end fraction space space space space equals 0.083 space bar space dm cubed space straight K to the power of negative 1 end exponent space mol to the power of negative 1 end exponent$

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States Of Matter

Write the units of the gas constant R in different scales of measurement ?

Some More Questions From States of Matter Chapter

How is the pressure of a gas related to the number of molecules of the gas at constant temperature and volume?

What is standard (or normal) temperature and pressure (STP)?

What does SATP stand for? Define it.

What is the value of molar volume at STP?

What is standard molar volume?

What is the value of gas constant in SI units?

What is meant by aqueous tension?

What is the nature of gas consant R?

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