# Solved problems on Ideal gas law

**Example (1): Calculate the volume of a sample of gas originally occupying 908 mL at 717 torr and 20**

^{o}C after its temperature and pressure are changed to 72^{o}C and 1.07 atm.**Solution**

Again,
tabulating the data is a good idea.

The volume can
be stated in milliliters in both states.

The pressure
can be stated in atmospheres in both.

The temperature
must be in kelvins in both states; it cannot merely be in the same unit in both
states.

**Example (2): A 17.3-mL sample of gas originally at standard temperature and pressure is changed to 10.9 mL at 678 torr. Calculate its final temperature in degrees Celsius.**

**Solution**

**Example (3): Calculate the volume of 1.63 mol of carbon dioxide gas at 295 K and 1.14 atm.**

**Solution**

**Example (4): Calculate the volume of 42.6 g of oxygen gas at 35**

^{o}C and 792 torr.**Solution**

Because the
value of R given previously has units of liters, atmospheres, moles, and
kelvins, the data given here are converted to these units:

**Example (5): Decide which gas law should be used to solve each of the following:**

**(a) Calculate the final volume of a sample of gas that has an initial volume of 7.10 L at STP if the temperature and pressure are changed to 33**

^{o}C and 696 torr.**(b) Calculate the volume of 0.977 mol of gas at 33**

^{o}C and 792 torr.**Solution**

(a) The
combined gas law can be used.

(b) This
problem involves moles and must be solved with the ideal gas law

**Example(6): Calculate the volume of 12.7 g of water at 25**

^{o}C and 1.00 atm.**Solution**

The density of
liquid water is 1.00 g/mL, and thus the volume is 12.7 mL.

Not only the
laws, but also when to use each one, must be learned.

**Example (7): Calculate the pressure of 0.0789 mol of chlorine gas that occupies 891 mL at -15°C.**

**Solution**

The quantities given are converted to the units generally used with
the ideal gas law equation.

Note that the nature of the gas is immaterial as long as the number
of moles is known.

**Example (8): Calculate the number of moles of oxygen gas in a 2.60-L container at 19**

^{o}C and 755 torr.

**Solution**

**Example (9): An inflated helium balloon with a volume of 0.55 L at sea level (1.0 atm) is allowed to rise to a height of 6.5 km, where the pressure is about 0.40 atm. Assuming that the temperature remains constant, what is the final volume of the balloon?**

**solution:**

Because n

_{1}= n_{2}and T_{1}= T_{2},
which is Boyle’s law. The given information is tabulated:

**Example (10): Argon is an inert gas used in light bulbs to retard the vaporization of the tungsten filament. A certain light bulb containing argon at 1.20 atm and 18**

^{o}C is heated to 85^{o}C at constant volume. Calculate its final pressure (in atm).**Solution:**

from combined gas law:

Because n

_{1}= n_{2}and V_{1}= V_{2}, the Equation becomes:
which is Charles’s law. Next we write

**Example (11): A small bubble rises from the bottom of a lake, where the temperature and pressure are 8**

^{o}C and 6.4 atm, to the water’s surface, where the temperature is 25^{o}C and the pressure is 1.0 atm. Calculate the final volume (in mL) of the bubble if its initial volume was 2.1 mL.

**Solution**:

According to combined gas law Equation:

The given information is summarized:

*Reference:*

*Chemistry*

*/ Raymond Chang ,*

*Williams College*

*/*

*(10th edition).*

*Fundamentals of Chemistry*

*/ David E.Goldberg*

*/*

*(5th edition).*

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