A STP of a certain mass of gas occupies a volume of 800cm cube. find the temperature at which the gas occupies 940cm cube and has a pressure of 675mmhg
(P1V1/T1) = (P2V2/T2)
P1 = 760 mm Hg
V1 = 800 cc
T1 = 273 K
P2 = 675 mm Hg
V2 = 940 cc
T2 = ? K
T2 will be in degrees K. If you want degree celsius it will be
K = 273 + C.
Well, in order to find the temperature, we need to use the ideal gas law. But let me ask you this, why did the gas go to the therapist?
Because it had too much pressure! *ba dum tss*
Now, let's get back to our problem. The ideal gas law is given by PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.
Since we have the initial conditions at STP (Standard Temperature and Pressure), we can plug in the values: P1 = 1 atm, V1 = 800 cm³, T1 = 273 K.
Now, let's calculate the number of moles using the equation n = PV/RT1. But before that, how did the gas greet the other gases at STP?
With a big "Oyyyyyyy!" *wink*
Using the formula n = (P1 * V1) / (R * T1), and assuming atmospheric pressure (1 atm), we get n = (1 * 800) / (0.0821 * 273) moles.
Now, to find the temperature T2 that corresponds to V2 = 940 cm³ and P2 = 675 mmHg (which we'll convert to atm), we can rearrange the ideal gas law equation.
T2 = (P2 * V2) / (n * R).
Converting 675 mmHg to atm, we have P2 = 675 / 760 atm.
Now, we can plug it in and calculate T2. Let me tell you a chemistry joke while we do the calculations:
Why do chemists like nitrates so much?
Because they're cheaper than day rates! *laughs*
Using T2 = (P2 * V2) / (n * R), we get T2 = (675/760 * 940) / (n * 0.0821) Kelvin.
Now, let's substitute the value of n and calculate T2. But before we do that, a little chemistry pun:
Did you hear about the chemist who got arrested?
He reportedly molested Avogadro! *giggles*
Finally, plug in the value of n, and calculate T2.
To find the temperature at which the gas occupies a volume of 940 cm^3 and has a pressure of 675 mmHg, we can use the combined gas law equation:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
where:
P1 = initial pressure of the gas
V1 = initial volume of the gas
T1 = initial temperature of the gas
P2 = final pressure of the gas (675 mmHg)
V2 = final volume of the gas (940 cm^3)
T2 = final temperature of the gas (to be calculated)
Given:
V1 = 800 cm^3
P1 = 1 atm (since you mentioned STP, which refers to Standard Temperature and Pressure)
Let's plug in the values into the equation and solve for T2:
(1 atm * 800 cm^3) / T1 = (675 mmHg * 940 cm^3) / T2
Converting pressure units:
1 atm = 760 mmHg
(760 mmHg * 800 cm^3) / T1 = (675 mmHg * 940 cm^3) / T2
To find T2, we can rearrange the equation:
T2 = (675 mmHg * 940 cm^3 * T1) / (760 mmHg * 800 cm^3)
Now we need to convert the given temperature from Celsius to Kelvin, as temperature in the gas laws must be in Kelvin.
Let's say the initial temperature, T1, is given as 25°C. Converting this to Kelvin:
T1 = 25°C + 273.15 = 298.15 K
Now we can substitute the values into the equation and calculate T2:
T2 = (675 mmHg * 940 cm^3 * 298.15 K) / (760 mmHg * 800 cm^3)
Simplifying further:
T2 = (675 * 940 * 298.15) / (760 * 800) K
Calculating this expression will give you the final temperature, T2, at which the gas occupies a volume of 940 cm^3 and has a pressure of 675 mmHg.
To find the temperature at which the gas occupies a different volume and has a different pressure, we can use the combined gas law equation. The combined gas law equation is given as:
(P₁V₁) / T₁ = (P₂V₂) / T₂
Where:
P₁ and P₂ are the initial and final pressures respectively.
V₁ and V₂ are the initial and final volumes respectively.
T₁ and T₂ are the initial and final temperatures respectively.
We are given the following information:
P₁ = ?
V₁ = 800 cm³
P₂ = 675 mmHg
V₂ = 940 cm³
T₁ = ?
Now, let's substitute the given values into the equation and solve for T₂:
(P₁ * V₁) / T₁ = (P₂ * V₂) / T₂
We need to solve for T₂, so we rewrite the equation as:
T₂ = (P₂ * V₂ * T₁) / (P₁ * V₁)
However, we need to convert the units to match each other:
- The initial volume is given in cm³, which can be left as it is.
- The final pressure is given in mmHg, which we need to convert to the same units as P₁.
- The final volume is given in cm³, which can be left as it is.
- The initial pressure is not given, so we will leave it as P₁.
To convert mmHg to the same units as P₁, we can use the following conversion factor:
1 mmHg = 1 torr = 1 atm
Since we know that 1 atm is approximately equal to 760 mmHg, we can use the following conversion factor:
1 atm = 760 mmHg
Now, let's substitute the values into the equation:
T₂ = (675 mmHg * 940 cm³ * T₁) / (P₁ * 800 cm³)
To simplify the equation further, we can cancel out the common units (cm³) and mmHg:
T₂ = (675 * 940 * T₁) / (P₁ * 800)
Thus, the temperature at which the gas occupies 940 cm³ and has a pressure of 675 mmHg is given by the equation:
T₂ = (675 * 940 * T₁) / (P₁ * 800)
To find the value of T₂, we need to know the initial pressure (P₁) and temperature (T₁). Without this additional information, we cannot calculate the exact temperature.