Determine the final pressure of a gas that has an initial pressure of 1.00 atm and is heated from 20 °C to 30 °C. Round to the nearest hundredth. Don't forget the units.
(V1/T1) = (V2/T2)
Don't forget T must be in kelvin.
To determine the final pressure of a gas that is heated, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure of the gas
V = volume of the gas
n = number of moles of the gas
R = ideal gas constant (0.0821 L*atm/mol*K)
T = temperature of the gas in Kelvin
To solve this problem, we need to convert the initial and final temperatures from Celsius to Kelvin:
Initial temperature, T1 = 20 °C + 273.15 = 293.15 K
Final temperature, T2 = 30 °C + 273.15 = 303.15 K
Since the volume and the number of moles of the gas are not specified, we can assume that they remain constant. Therefore, we can rewrite the ideal gas equation as:
P1/T1 = P2/T2
Now, we can substitute the given values into the equation:
P1 = 1.00 atm
T1 = 293.15 K
T2 = 303.15 K
Plugging in these values, we get:
1.00 atm / 293.15 K = P2 / 303.15 K
To find P2, we cross multiply and solve for P2:
P2 = (1.00 atm * 303.15 K) / 293.15 K
P2 ≈ 1.03 atm
Therefore, the final pressure of the gas, rounded to the nearest hundredth, is approximately 1.03 atm.