3. suppose a gas at STP. Calculate its pressure at 25 degrees celcius if volume remains unchanged
5. suppose 1.11 L of an unknown gas in a rigid container constant volume is cooled from 22 deg. C to -55 deg C. Calculate the new pressure of the gas
6.) Suppose a 50.0 cm ^3 sample of gas is collected at 27 deg C. Calculate the volume of the gas if it is cooled to -3 deg C under constant pressure
P1 V1/T1 = P2 V2/T2 = n R
T1 = 0 +273 = 273
T2 = 25 + 273 = 298
P2/P1 = T2/T1
= 298/273
The other questions are the same deal.
To answer these questions, 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
T = temperature of the gas in Kelvin
To calculate the pressure at different temperatures (questions 3, 5, and 6), we need to keep the volume constant, which means V remains the same in the equation.
Let's go through each question step by step to find the answers:
3. To calculate the pressure at 25 degrees Celsius while keeping the volume constant, we convert the temperature to Kelvin (K):
T(K) = T(°C) + 273.15
T(K) = 25 + 273.15 = 298.15 K
Since the volume is constant, V remains the same in the equation. We can rearrange the equation to solve for P:
P = (nRT) / V
At STP (Standard Temperature and Pressure), 1 mole of gas occupies 22.4 L of volume. So we can assume n = 1 mole and V = 22.4 L.
Plugging in the values, we get:
P = (1 mole * R * 298.15 K) / 22.4 L
Using the value of R = 0.0821 L·atm/(mol·K), we can calculate the pressure:
P = (1 * 0.0821 * 298.15) / 22.4
P ≈ 1.097 atm
Therefore, the pressure at 25 degrees Celsius is approximately 1.097 atm.
5. To calculate the new pressure of the gas when it is cooled from 22°C to -55°C with constant volume, we need to convert both temperatures to Kelvin:
T1(K) = 22 + 273.15 = 295.15 K
T2(K) = -55 + 273.15 = 218.15 K
Again, since the volume is constant, V remains the same. We can use the same formula as before:
P1 / T1 = P2 / T2
Rearranging for P2:
P2 = (P1 * T2) / T1
Using the initial pressure P1 and the temperatures T1 and T2, we can calculate the new pressure:
P2 ≈ (P1 * 218.15) / 295.15
6. In this question, we need to calculate the new volume of the gas when it is cooled from 27°C to -3°C under constant pressure.
Again, we convert both temperatures to Kelvin:
T1(K) = 27 + 273.15 = 300.15 K
T2(K) = -3 + 273.15 = 270.15 K
Since the pressure is constant, we can rearrange the equation to find the new volume:
V2 = (V1 * T2) / T1
Using the initial volume V1 and the temperatures T1 and T2, we can calculate the new volume:
V2 = (V1 * 270.15) / 300.15
Remember to always use Kelvin for temperature when using the ideal gas law equation.