At STP,a certain mass of gas occupied a volume of 790cm³,find the temperature at which the gas occupied 1000cm³ and has a pressure of 728mmhg
PV=kT, so PV/T = k, a constant.
Now, STP has
T = 273.15
P = 1 atm = 760mmHg
Thus, you want T such that
728*1000/T = 760*790/273.15
Some like to use P1V1/T1 = P2V2/T2
Solve me this calculation
To find the temperature at which a gas occupies a certain volume and has a given pressure, we can use the combined gas law equation:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
P1 = Pressure 1 (in mmHg)
V1 = Volume 1 (in cm³)
T1 = Temperature 1 (in Kelvin)
P2 = Pressure 2 (in mmHg)
V2 = Volume 2 (in cm³)
T2 = Temperature 2 (in Kelvin)
First, let's convert the given values to the required units:
P1 = 760 mmHg (standard pressure at STP)
V1 = 790 cm³
V2 = 1000 cm³
P2 = 728 mmHg
Now, we need to rearrange the equation to solve for T2 (Temperature 2):
T2 = (P2 * V2 * T1) / (P1 * V1)
Substituting the values we have:
T2 = (728 mmHg * 1000 cm³ * T1) / (760 mmHg * 790 cm³)
Now, we need to convert the units:
1 cm³ = 1 mL
1 L = 1000 cm³
1 mmHg = 1 torr
1 atm = 760 mmHg
T2 = (728 torr * 1 L * T1) / (760 torr * 790 mL)
Note: You may also need to convert the temperatures to Kelvin if they are given in Celsius. Use the conversion formula T(K) = T(°C) + 273.15.
Finally, substitute the given values into the equation and solve for T2:
T2 = (728 * 1 * T1) / (760 * 790)
= (T1 / 790.84)
Therefore, the temperature at which the gas occupies 1000 cm³ and has a pressure of 728 mmHg is T2 = T1 / 790.84 (in Kelvin).