At s.t.p a certain mass of gas occupies a volume of 790cm 2. Find the temperature of at which the gas occupies 1000cm 3 atm has a pressure of 726 mmHg
PV=kT, so PV/T is constant.
So, you want to find T such that
726*1000/T = 760*790/273
To find the temperature at which the gas occupies a volume of 1000 cm3 at a pressure of 726 mmHg in standard temperature and pressure (STP), we can use the combined gas law equation.
The combined gas law equation is given by:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 = initial pressure
V1 = initial volume
T1 = initial temperature
P2 = final pressure
V2 = final volume
T2 = final temperature
We are given:
P1 = 1 atm (since it's at STP)
V1 = 790 cm3
P2 = 726 mmHg (which can be converted to atm by dividing by 760 mmHg/atm)
V2 = 1000 cm3
Converting 726 mmHg to atm:
726 mmHg / 760 mmHg/atm = 0.955 atm
Substituting the given values into the equation, we have:
(1 atm * 790 cm3) / (T1) = (0.955 atm * 1000 cm3) / (T2)
Simplifying the equation, we get:
790 cm3 / T1 = 955 cm3 / T2
Cross-multiplying the equation, we have:
790 cm3 * T2 = 955 cm3 * T1
Dividing both sides by 790 cm3, we get:
T2 = (955 cm3 * T1) / 790 cm3
Now, since we are looking for the temperature T2, we need to solve for T2. To do this, we need to substitute a known value for T1. Since the gas is at STP, the temperature is 273.15 Kelvin (0 degrees Celsius).
Substituting T1 = 273.15 K, we have:
T2 = (955 cm3 * 273.15 K) / 790 cm3
Calculating the resulting temperature, we get:
T2 ≈ 330.47 K
Therefore, the temperature at which the gas occupies a volume of 1000 cm3 at a pressure of 726 mmHg in STP is approximately 330.47 Kelvin.