SHOW WORK
A cylinder containing 48g of nitrogen gas at room temperature is placed on a scale. The valve is opened and 12g of gas are allowed to escape. Assuming that the temperature of the cylinder remains constant, how does the pressure change?
12/48 = 0.25 or 25% so the pressure will be reduced by 25% (or another way to say it is that the pressure will be 75% of the original).
So if the original P = 1 atmosphere, the new P would be 0.75 atm or if the original P = 2 atm the new P = 1.5 atm etc.
To determine how the pressure changes when 12g of nitrogen gas are allowed to escape from the cylinder, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
Since the temperature remains constant, we can consider it as a constant value. Thus, the equation can be rearranged as:
P = (nRT) / V
The number of moles (n) can be calculated using the equation:
n = m / M
Where:
m = mass of the gas
M = molar mass of the gas
Given that the initial mass of nitrogen gas is 48g, we can calculate the initial number of moles:
n_initial = 48g / M_nitrogen
Next, we need to determine the final number of moles after 12g of gas escape. We can subtract the mass lost (12g) from the initial mass (48g) to find the final mass:
m_final = 48g - 12g = 36g
Then, we can calculate the final number of moles:
n_final = 36g / M_nitrogen
Since the initial and final volume (V) do not change, we can cancel it out when comparing the initial and final pressures:
P_initial / P_final = (n_initial / n_final) * (M_nitrogen / M_nitrogen)
Since the molar mass of nitrogen gas (M_nitrogen) is the same on both sides of the equation, we can simplify it further:
P_initial / P_final = (n_initial / n_final)
Plugging in the values, we get:
P_initial / P_final = (48g / M_nitrogen) / (36g / M_nitrogen) = 48g / 36g = 4/3
Therefore, the pressure decreases by a factor of 4/3 or 1.33 (approximately). Thus, the pressure decreases by about 1.33 times when 12g of nitrogen gas are allowed to escape from the cylinder while the temperature remains constant.