1. Prove that Boyle’s Law exist by indicating that the volume (375.35 mL) at 1.85 atm pressure increases if we decrease the pressure by half.
Ans: 750.7 mL
2. What is the final temperature (in Fahrenheit) at 43.85 mL if the initial temperature at 78.35 is 2988.15 K?
Ans: -159.31 oF
3. Prove that an 8 oz coke (P = 9.85 atm) has lesser pressure than 12 oz?
Ans: Unable to prove since the P at 12 oz is 0.57 atm. It violates the Law
4. Find the moles of a perfect gas if the pressure is 1385 mmHg with a volume of 500 mL at a temperature of 175 oF.
Ans: 0.03 moles
5. Iceman produced an ice cube with a density of 0.95 g/mL and a mass of 25.35 g. If the original volume of the ice is 283.45 mL at 2.75 moles, what is the original number of moles of the ice?
Ans: 0.00364 moles
6. An inflatable balloon at 35 oC can accommodate 32 L of gas. How much temperature is needed to fill the balloon with 1,785 L of gas?
Ans: 1952.34 oC
7. An ideal gas originally has 2222 mmHg pressure, 235 mL volume, and 0.85 moles at 37 oC. If the pressure and volume are doubled, and the mole increased by 75%, what is the final temperature?
Ans: 708.91 K
8. What is the pressure (mmHg) of an 8 oz ideal gas if the number of moles present at 28 oC is 0.5 moles? (1 oz = 29.6 mL)
Ans: 39,676.00 mmHg
9. How much did the volume increases (in %) at 38 oC if the original volume at 29 oC is 32 mL?
Ans: 23.68 % (volume is 41.93 mL)
10. Construct a data for Pressure, volume temperature and number of moles for an ideal gas. Use the ideal gas equation.
Ans: Any data would do as long as the final answer for PV/nT is 0.0821
MERRY CHRISTMAS AND HAPPY NEW YEAR TO ALL!!!
Friday, December 25, 2009
Thursday, December 3, 2009
GAS LAWS
Gas laws
The early gas laws were developed at the end of the eighteenth century, when scientists began to realize that relationships between the pressure, volume and temperature of a sample of gas could be obtained which would hold for all gases. Gases behave in a similar way over a wide variety of conditions because to a good approximation they all have molecules which are widely spaced, and nowadays the equation of state for an ideal gas is derived from kinetic theory. The earlier gas laws are now considered as special cases of the ideal gas equation, with one or more of the variables held constant.
Boyle's Law
Boyle's Law shows that, at constant temperature, the product of an ideal gas's pressure and volume is always constant. It was published in 1622. It can be determined experimentally using a pressure gauge and a variable volume container. It can also be found logically; if a container with a fixed amount of molecules inside it is reduced in volume, more molecules will hit the sides of the container per unit time causing a greater pressure.
As a mathematical equation, Boyle's law is:
Where P is the pressure (Pa) and V the volume (m3) of a gas. k1 (measured in joules) is the constant from this equation- it is not the same as the constants from the other equations below.
Charles' Law
Charle's Law, or the law of volumes, was found in 1787. It says that, for an ideal gas at constant pressure, the volume is proportional to the absolute temperature (in Kelvin). This can be found using the kinetic theory of gases or a heated container with a variable volume (such as a conical flask with a balloon).
Where T is the absolute temperature of the gas (in Kelvin) and k2 (in m3 K−1) is the constant produced.
Pressure Law (Gay-Lussac’s Law)
The pressure (or Gay-Lussac's) law was found by Joseph Louis Gay-Lussac in 1809. It states that the pressure exerted on a container's sides by an ideal gas is proportional to the absolute temperature of the gas. This follows from the kinetic theory- by increasing the temperature of the gas, the molecules' speeds increase meaning an increased amount of collisions with the container walls.
As a mathematical formula, this is:
Avogadro's Law
Avogadro's Law states that the volume occupied by an ideal gas is proportional to the amount of moles (or molecules) present in the container. This gives rise to the molar volume of a gas, which at STP is 22.4 dm3 (or liters).
Where n is equal to the number of moles of gas (the number of molecules divided by Avogadro's Number).
Ideal gas laws
The combined gas law or general gas equation is formed by the combination of the three laws, and shows the relationship between the pressure, volume and temperature for a fixed mass of gas:
With the addition of Avogadro's law, the combined gas law develops into the ideal gas law:
Where R is the gas constant with a value of 0.0821 L-atm/K-mol
An equivalent formulation of this law is:
where
N is the number of molecules.
These equations are exact only for an ideal gas, which neglects various intermolecular effects (see real gas). However, the ideal gas law is a good approximation for most gases under moderate pressure and temperature.
This law has the following important consequences:
1. If temperature and pressure are kept constant, then the volume of the gas is directly proportional to the number of molecules of gas.
2. If the temperature and volume remain constant, then the pressure of the gas changes is directly proportional to the number of molecules of gas present.
3. If the number of gas molecules and the temperature remain constant, then the pressure is inversely proportional to the volume.
4. If the temperature changes and the number of gas molecules are kept constant, then either pressure or volume (or both) will change in direct proportion to the temperature.
The early gas laws were developed at the end of the eighteenth century, when scientists began to realize that relationships between the pressure, volume and temperature of a sample of gas could be obtained which would hold for all gases. Gases behave in a similar way over a wide variety of conditions because to a good approximation they all have molecules which are widely spaced, and nowadays the equation of state for an ideal gas is derived from kinetic theory. The earlier gas laws are now considered as special cases of the ideal gas equation, with one or more of the variables held constant.
Boyle's Law
Boyle's Law shows that, at constant temperature, the product of an ideal gas's pressure and volume is always constant. It was published in 1622. It can be determined experimentally using a pressure gauge and a variable volume container. It can also be found logically; if a container with a fixed amount of molecules inside it is reduced in volume, more molecules will hit the sides of the container per unit time causing a greater pressure.
As a mathematical equation, Boyle's law is:
Where P is the pressure (Pa) and V the volume (m3) of a gas. k1 (measured in joules) is the constant from this equation- it is not the same as the constants from the other equations below.
Charles' Law
Charle's Law, or the law of volumes, was found in 1787. It says that, for an ideal gas at constant pressure, the volume is proportional to the absolute temperature (in Kelvin). This can be found using the kinetic theory of gases or a heated container with a variable volume (such as a conical flask with a balloon).
Where T is the absolute temperature of the gas (in Kelvin) and k2 (in m3 K−1) is the constant produced.
Pressure Law (Gay-Lussac’s Law)
The pressure (or Gay-Lussac's) law was found by Joseph Louis Gay-Lussac in 1809. It states that the pressure exerted on a container's sides by an ideal gas is proportional to the absolute temperature of the gas. This follows from the kinetic theory- by increasing the temperature of the gas, the molecules' speeds increase meaning an increased amount of collisions with the container walls.
As a mathematical formula, this is:
Avogadro's Law
Avogadro's Law states that the volume occupied by an ideal gas is proportional to the amount of moles (or molecules) present in the container. This gives rise to the molar volume of a gas, which at STP is 22.4 dm3 (or liters).
Where n is equal to the number of moles of gas (the number of molecules divided by Avogadro's Number).
Ideal gas laws
The combined gas law or general gas equation is formed by the combination of the three laws, and shows the relationship between the pressure, volume and temperature for a fixed mass of gas:
With the addition of Avogadro's law, the combined gas law develops into the ideal gas law:
Where R is the gas constant with a value of 0.0821 L-atm/K-mol
An equivalent formulation of this law is:
where
N is the number of molecules.
These equations are exact only for an ideal gas, which neglects various intermolecular effects (see real gas). However, the ideal gas law is a good approximation for most gases under moderate pressure and temperature.
This law has the following important consequences:
1. If temperature and pressure are kept constant, then the volume of the gas is directly proportional to the number of molecules of gas.
2. If the temperature and volume remain constant, then the pressure of the gas changes is directly proportional to the number of molecules of gas present.
3. If the number of gas molecules and the temperature remain constant, then the pressure is inversely proportional to the volume.
4. If the temperature changes and the number of gas molecules are kept constant, then either pressure or volume (or both) will change in direct proportion to the temperature.
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