9. What should be the pressure of a gas if the volume of the gas at STP condition is
reduced by 80% keeping the temperature constant.?
10. At what initial pressure should have been a gas of 50 mL at 300 K if the pressure after
expansion by 10 times becomes 100 mm ?
Answers
So far, the gas laws we have considered have all required that the gas change its conditions; then we predict a resulting change in one of its properties. Are there any gas laws that relate the physical properties of a gas at any given time?
Consider a further extension of the combined gas law to include n. By analogy to Avogadro’s law, n is positioned in the denominator of the fraction, opposite the volume. So
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Because pressure, volume, temperature, and amount are the only four independent physical properties of a gas, the constant in the above equation is truly a constant; indeed, because we do not need to specify the identity of a gas to apply the gas laws, this constant is the same for all gases. We define this constant with the symbol R, so the previous equation is written as
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which is usually rearranged as
PV = nRT
This equation is called the ideal gas law. It relates the four independent properties of a gas at any time. The constant R is called the ideal gas law constant. Its value depends on the units used to express pressure and volume. Table 6.1 “Values of the Ideal Gas Law Constant R“ lists the numerical values of R.
Table 6.1 Values of the Ideal Gas Law Constant R
Numerical Value Units
0.08205 L·atm/mol·K
62.36 L·torr/mol·K = L·mmHg/mol·K
8.314 J/mol·K
The ideal gas law is used like any other gas law, with attention paid to the units and making sure that temperature is expressed in kelvins. However, the ideal gas law does not require a change in the conditions of a gas sample. The ideal gas law implies that if you know any three of the physical properties of a gas, you can calculate the fourth property.