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fandomhigh2006-01-19 09:06 am
equalsmcsquared.livejournal.com) wrote in fandomhigh2006-01-19 09:06 am
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Chemistry (4th Period)
"Good morning. Please turned in the homework I assigned last time."
The Combined Gas Law is a combination of Boyle's and Charles' Laws. The Combined Gas Law describes the relationship between pressure, volume, and temperature. For example, if the pressure increased, wither the volume would decrease or the temperature would increase.
The Combined Gas Law can be used to solve any Boyle's or Charles' Law problem. If one of the variables remains constant, disregard that variable by leaving it out of your equation or setting it to the same value on either side of the equals sign.
The pressure and volume of a gas are inversely proportional to each other, but directly proportional to the temperature of that gas.
Mathematically, this can be represented as:
Temperature = Volume x Pressure / Constant
or
Volume = Constant x Temperature / Pressure
or
Pressure = Constant x Temperature / Volume
or
Pressure x Volume/Temperature = Constant
Substituting in variables, the formula is:
PV/T=K
Because the formula is equal to a constant, it is possible to solve for a change in volume, temperature, or pressure using a proportion:
PV/T = P1V1/T1
Let's try a problem with the Combined Gas Law. For example, the pressure and temperature of a gas are changed to STP (101.3 kPa/0°C) from 22.0°C and 30.8 kPa. What will be the new volume if the original volume was 205 mL?
First, we must convert degrees Celcius to Kelvins. This means that our original temperature was 295 K and our target temperature is 273 K.
It seems that the pressure increases, but the temperature decreases. Because of their inverse relationship, the increased pressure will decrease the volume. Because of their direct relationship, the decreased temperature will decrease the volume, also. If we consider the amount that the pressure increases, it more than triples. The temperature decreases only slightly. Therefore, it is safe to assume that the new volume will be less than a third of its original volume, or less than 68.2 mL (205 x 0.3333 = 68.2).
Plug values into the formula
From the problem, we know that, for the original state of the gas, the conditions were:
Volume (V) = 205 mL
Temperature (T) = 295 K
Pressure (P) = 30.8 kPa
We also know the target temperature and pressure:
Temperature1 (T1) = 273 K K
Pressure1 (P1) = 101.3 kPa
The unkown is V1. Our equation is:
30.8 kPa x 205 mL / 295 K = 101.3 kPa x V1 / 273 K
Manipulating the equation, we get:
V1 = 30.8 kPa x 205 mL / 295 K x 273 K / 101.3 kPa
V1 = 57.68 mL
However, because our problem only was to three digits of precision, the answer is:
V1 = 57.7 mL
To check our answer, we must compare it to our earlier estimate. We estimated the value to be less than 68.2 mL. Because 57.7 mL is less than 68.2 mL, but not incredible much so (like 20 - 30 mL), we can assume the answer to be correct.
Homework: Please do the problems listed on page 33 of your textbook and be ready to discuss them next week. Have a nice day.
The Combined Gas Law is a combination of Boyle's and Charles' Laws. The Combined Gas Law describes the relationship between pressure, volume, and temperature. For example, if the pressure increased, wither the volume would decrease or the temperature would increase.
The Combined Gas Law can be used to solve any Boyle's or Charles' Law problem. If one of the variables remains constant, disregard that variable by leaving it out of your equation or setting it to the same value on either side of the equals sign.
The pressure and volume of a gas are inversely proportional to each other, but directly proportional to the temperature of that gas.
Mathematically, this can be represented as:
Temperature = Volume x Pressure / Constant
or
Volume = Constant x Temperature / Pressure
or
Pressure = Constant x Temperature / Volume
or
Pressure x Volume/Temperature = Constant
Substituting in variables, the formula is:
PV/T=K
Because the formula is equal to a constant, it is possible to solve for a change in volume, temperature, or pressure using a proportion:
PV/T = P1V1/T1
Let's try a problem with the Combined Gas Law. For example, the pressure and temperature of a gas are changed to STP (101.3 kPa/0°C) from 22.0°C and 30.8 kPa. What will be the new volume if the original volume was 205 mL?
First, we must convert degrees Celcius to Kelvins. This means that our original temperature was 295 K and our target temperature is 273 K.
It seems that the pressure increases, but the temperature decreases. Because of their inverse relationship, the increased pressure will decrease the volume. Because of their direct relationship, the decreased temperature will decrease the volume, also. If we consider the amount that the pressure increases, it more than triples. The temperature decreases only slightly. Therefore, it is safe to assume that the new volume will be less than a third of its original volume, or less than 68.2 mL (205 x 0.3333 = 68.2).
Plug values into the formula
From the problem, we know that, for the original state of the gas, the conditions were:
Volume (V) = 205 mL
Temperature (T) = 295 K
Pressure (P) = 30.8 kPa
We also know the target temperature and pressure:
Temperature1 (T1) = 273 K K
Pressure1 (P1) = 101.3 kPa
The unkown is V1. Our equation is:
30.8 kPa x 205 mL / 295 K = 101.3 kPa x V1 / 273 K
Manipulating the equation, we get:
V1 = 30.8 kPa x 205 mL / 295 K x 273 K / 101.3 kPa
V1 = 57.68 mL
However, because our problem only was to three digits of precision, the answer is:
V1 = 57.7 mL
To check our answer, we must compare it to our earlier estimate. We estimated the value to be less than 68.2 mL. Because 57.7 mL is less than 68.2 mL, but not incredible much so (like 20 - 30 mL), we can assume the answer to be correct.
Homework: Please do the problems listed on page 33 of your textbook and be ready to discuss them next week. Have a nice day.
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