A sample of nitrogen occupies a volume of 300ml under a pressure of 380 torr at -177C. What would be the volume at STP?
I know the answer is 430mL but I don't know which equations to use to formulate the calculation.
You have two sets of P, T, V.
(P1V1/T1) = (P2V2/T2)
ADh1
To find the volume of nitrogen at Standard Temperature and Pressure (STP), we can use Boyle's Law and the Ideal Gas Law.
Step 1: Convert the temperature from Celsius to Kelvin.
Since the temperature is -177°C, we need to add 273.15 to convert it to Kelvin.
-177°C + 273.15 = 96.15 K
Step 2: Apply Boyle's Law.
Boyle's Law states that the pressure and volume of a gas are inversely proportional, assuming constant temperature.
P1 * V1 = P2 * V2
Where:
P1 = initial pressure (380 torr)
V1 = initial volume (300 mL)
P2 = final pressure (STP pressure, which is 1 atm or 760 torr)
V2 = final volume (unknown, which we need to find)
Substituting the values:
380 torr * 300 mL = 760 torr * V2
Step 3: Solve for V2.
V2 = (380 torr * 300 mL) / 760 torr
V2 = 150,000 torr mL / 760 torr
V2 = 197.37 mL
Therefore, the volume of nitrogen at STP would be approximately 197.37 mL, not 430 mL as mentioned in your question. Please double-check your answer.
To solve this problem, you can use the ideal gas law, which states that:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
To find the volume at STP (Standard Temperature and Pressure), you need to determine the number of moles of nitrogen first using the given information. We can use the ideal gas law rearranged to solve for n:
n = PV / RT
At this point, we can convert the given temperature to Kelvin since the gas law requires temperature in Kelvin. The conversion from Celsius to Kelvin is as follows:
T(K) = T(C) + 273.15
Now we can plug in the values into the equation and calculate the number of moles:
n = (380 torr) * (300 mL) / (0.0821 L·atm/mol·K) * (96.15 K)
This will give you the number of moles of nitrogen. Since the volume is directly proportional to the number of moles under constant temperature and pressure, you can use the stoichiometry of the ideal gas law to find the volume at STP.
However, you mentioned that you already know the answer is 430 mL. Assuming this is correct, we can calculate the ratio of the volumes at the given conditions and the desired STP conditions:
V2 / 300 mL = 430 mL / V1
Now you can solve for V1:
V1 = (V2 * 300 mL) / 430 mL
Substituting V2 = 430 mL, you can calculate:
V1 = (430 mL * 300 mL) / 430 mL
V1 = 300 mL
So, according to the given information and calculation, the volume of the nitrogen sample at STP would also be 300 mL, not 430 mL. If you have specific calculations or information that leads to a different answer, please provide them for further assistance.