Charles's law of gases indicates that, at a constant pressure, the volume of a gas is proportional to the temperature. This is calculated by the following equation:

$\displaystyle \frac{V_1}{T_1}=\frac{V_2}{T_2}$

Our first step to solving this equation will be to convert the given temperature to Kelvin.

$\displaystyle 82^oC+273=355K$

Using this temperature and the given volumes, we can solve for the final temperature of the gas.

$\displaystyle \frac{7.82L}{355K}=\frac{6.45L}{T_2}$

$\displaystyle T_2=\frac{(355K)(6.45L)}{7.82L}$

$\displaystyle T_2=293K$

The graph shows that there is a directly proportional relationship between the volume of a gas and temperature in Kelvin when kept at a constant pressure. This is known as Charles’s law and can be represented mathematically as follows:

$\displaystyle \frac{V_1}{T_1}=\frac{V_2}{T_2}$

Gay-Lussac's law shows the relationship between pressure and temperature. Boyle's law shows the relationship between pressure and volume. Newton's third law is not related to gas principles and states that for every force on an object, there is an equal and opposite force of the object on the source of force.

We expect the volume to increase since volume and temperature are directly proportional. We know that if we heat something the material will expand so we shouldn't get a value that is smaller than our initial volume. Charles Law says that

$\displaystyle \frac{V_{1}}{T_{1}}=\frac{V_{2}}{T_{2}}$

where the stuff on the left is the initial volume and temperature and the stuff on the right is the final volume and temperature. First off, we MUST convert the temperatures to Kelvin to use Charles Law. This gives

$\displaystyle T_{1}=22.0^{o}C+273=295K$

$\displaystyle T_{2}=36.6^{o}C+273=309.6K$

Solving for the final volume,

$\displaystyle V_{2}=\frac{V_{1}T_{2}}{T_{1}}$

$\displaystyle V_{2}=\frac{(50.2\,mL)(309.6K)}{(295K)}=52.7\,mL$

Since the volume of the gas is the only variable that has changed, we can use Boyle's law in order to find the final pressure. Since pressure and volume are on the same side of the ideal gas law, they are inversely proportional to one another. In other words, as one increases, the other will decrease, and vice versa.

Boyle's law can be written as follows:

$\displaystyle P_{1}V_{1} = P_{2}V_{2}$

Use the given volumes and the initial pressure to solve for the final pressure.

$\displaystyle (3atm)(3L) = (2L)P_{2}$

$\displaystyle P_{2} = 4.5atm$

Boyle's law relates the pressure and volume of a system, which are inversely proportional to one another. When the parameters of a system change, Boyle's law helps us anticipate the effect the changes have on pressure and volume.

$\displaystyle P_1V_1=P_2V_2$

Charles's law relates temperature and volume: $\displaystyle \frac{V_1}{T_1}=\frac{V_2}{T_2}$

Gay-Lussac's law relates temperature and pressure: $\displaystyle \frac{P_1}{T_1}=\frac{P_2}{T_2}$

The combined gas law takes Boyle's, Charles's, and Gay-Lussac's law and combines it into one law: $\displaystyle \frac{P_{1}V_{1}}{T_{1}}=\frac{P_{2} V_{2}}{T_{2}}$

The ideal gas law relates temperature, pressure, volume, and moles in coordination with the ideal gas constant: $\displaystyle PV=nRT$

To solve this question we will need to use Boyle's law:

$\displaystyle P_1V_2=P_2V_2$

We are given the final pressure and volume, along with the initial volume. Using these values, we can calculate the initial pressure.

$\displaystyle P_1(735mL)=(0.8atm)(1286mL)$

$\displaystyle P_1=\frac{(0.8atm)(1286mL)}{735mL}$

$\displaystyle P_1=1.4atm$

Note that the pressure at sea level is equal to $\displaystyle 1.0atm$. A pressure greater than $\displaystyle 1.0atm$ simply indicates that the ground level is below sea level at this point.

The graph shows that there is an inverse relationship between the volume and pressure of a gas, when kept at a constant temperature. This was described by Robert Boyle and can be represented mathematically as Boyle's law:

$\displaystyle P_1V_1=P_2V_2$

Gay-Lussac's law shows the relationship between pressure and temperature. Charles's law shows the relationship between volume and temperature. Hund's rule (Hund's law) is not related to gases, and states that electron orbitals of an element will be filled with single electrons before any electrons will form pairs within a single orbital.

To solve this question we will need to use Boyle's law:

$\displaystyle P_1V_2=P_2V_2$

We are given the initial pressure and volume, along with the final pressure. Using these values, we can calculate the final volume.

$\displaystyle (1.12atm)(225mL)=(0.98atm)V_2$

$\displaystyle V_2=\frac{(1.12atm)(225mL)}{0.98atm}$

$\displaystyle V_2=257mL$

Use Boyle's Law:

$\displaystyle P_1*V_1 = P_2*V_2$

Plug in known values and solve for final volume.

$\displaystyle 5L+1atm=3.5atm*V_2$

$\displaystyle V_2=1.43L$

Use Boyle's law and plug in appropriate parameters:

$\displaystyle P_1V_1=P_2V_2$

$\displaystyle .666L*1.03atm=5.68atm*V_2$

$\displaystyle \frac{.666L*1.03atm}{5.68L}=V_2$

$\displaystyle .121L=V_2$