At 122C the pressure of a sample of nitrogen gas is 0.830 atm. what will the temperature in Celsius be at 3.00 atm, assuming constant volume ?
(P1/T1) = (P2/T2). Don't forget to change temperature to Kelvin.
To find the temperature in Celsius at a pressure of 3.00 atm, assuming constant volume, we can use the combined gas law equation. The combined gas law relates the initial and final values of pressure (P1 and P2) and temperature (T1 and T2) of a gas sample when volume, in this case, is held constant.
The formula for the combined gas law is:
(P1 * T1) / (P2 * T2) = constant
Let's plug in the given values:
P1 = 0.830 atm
T1 = 122°C = (122 + 273.15) K (Converting Celsius to Kelvin)
P2 = 3.00 atm
T2 = ?
Now, let's rearrange the formula to solve for T2:
T2 = (P2 * (T1 * P1)) / (P1 * T2)
Plug in the given values:
T2 = (3.00 atm * ( (122 + 273.15) K * 0.830 atm)) / (0.830 atm * T2)
Simplify the equation by canceling out the common terms:
T2 = (3.00 atm * (122 + 273.15) K) / T2
Multiply both sides by T2 to isolate it:
T2^2 = (3.00 atm * (122 + 273.15) K)
Now, solve for T2 by taking the square root of both sides:
T2 = √(( 3.00 atm * (122 + 273.15) K))
Calculate the T2 value using the equation:
T2 = √((3.00 atm * (122 + 273.15) K))
T2 ≈ √(1601.85 atm·K) ≈ 40.03 K
To convert the temperature from Kelvin back to Celsius, subtract 273.15:
T2 ≈ 40.03 K - 273.15 ≈ -233.12°C
Therefore, the temperature in Celsius at 3.00 atm, assuming constant volume, would be approximately -233.12°C.