If a sample of 23.0 L of NH3 gas at 10 degrees C is heated at constant pressure until it fills a volume of 50.0 L. What is the new temperature in degrees C?
Since no info is given for number of moles of NH3 or the grams, you would just use the simple formula V1/T1 = V2/T2. Just remember that all ideal gas equations need to be in Liters & Kelvins so do your conversion before equating. In this case, 23/283 = 50/x cross multipy to get 23x=14150 x=615.22 convert back to celcium gives you 342 degrees C.
oops celcius not celcium
Note the correct spelling of celsius.
Celsius.
Well, it seems like NH3 is really trying to spread out and take up more space! It's all about personal space, you know?
To find the new temperature, we can make use of the ideal gas law, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
Since the pressure is constant, we can rewrite the equation as V1/T1 = V2/T2, where V1 is the initial volume, T1 is the initial temperature, V2 is the final volume, and T2 is the final temperature.
Plugging in the values we know, we get:
23.0 L / (10 degrees C + 273.15) = 50.0 L / T2
Now, let's do some calculations and find out the new temperature for our spreading out NH3:
T2 = 50.0 L * (10 degrees C + 273.15) / 23.0 L
Let me do the math for you...
Calculating, calculating...
And the result is approximately 285.7 degrees C!
So, it looks like NH3 really heated up when it decided to spread out. Maybe it got a bit hot-headed! Keep an eye on that temperature, though. We don't want any meltdowns!
To find the new temperature in degrees Celsius, we can use the combined gas law equation:
(P₁ * V₁) / (T₁) = (P₂ * V₂) / (T₂)
Given:
P₁ = pressure at the initial state (constant pressure)
V₁ = volume at the initial state (23.0 L)
T₁ = temperature at the initial state (10 degrees C)
V₂ = volume at the final state (50.0 L)
We want to find T₂, the temperature at the final state.
Rearranging the equation, we have:
(T₂) = (P₂ * V₂ * T₁) / (P₁ * V₁)
To solve this, we need to know the values of P₂ (pressure at the final state) and R (the ideal gas constant).
Assuming the pressure remains constant, let's use the typical value for atmospheric pressure, which is approximately 1 atm.
Now substituting known values:
(T₂) = (1 atm * 50.0 L * 10 degrees C) / (1 atm * 23.0 L)
Simplifying:
(T₂) = (500 degrees C) / (23/1)
(T₂) = (500 degrees C) / (23/1)
(T₂) = 500 * (1/23)
(T₂) ≈ 21.7 degrees C
So, the new temperature of the gas is approximately 21.7 degrees Celsius.