A fire extinguisher has a pressure of 13 atm at 25 °C.
What is the final pressure, in atmospheres, when the fire extinguisher is used at a temperature of 79°C, if V and n do not change?
Express your answer to two significant figures and include the appropriate units.
According to the ideal gas law, the pressure of a gas is directly proportional to its temperature, assuming all other variables remain constant. Thus, we can use the equation P1/T1 = P2/T2 to solve this problem, where P1 and T1 are the initial pressure and temperature, and P2 and T2 are the final pressure and temperature.
Given:
P1 = 13 atm
T1 = 25°C = 25 + 273.15 = 298.15 K
T2 = 79°C = 79 + 273.15 = 352.15 K
Substituting these values into the equation, we get:
P1/T1 = P2/T2
13 atm / 298.15 K = P2 / 352.15 K
Solving for P2:
P2 = (13 atm) * (352.15 K) / 298.15 K
P2 ≈ 15.36 atm
Rounding to two significant figures and including the appropriate units, the final pressure is approximately 15.36 atm.
To find the final pressure of the fire extinguisher when used at a temperature of 79 °C, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = gas constant
T = temperature
Given that the volume (V) and the number of moles (n) do not change, we can simplify the equation to:
P1/T1 = P2/T2
Where:
P1 = initial pressure
T1 = initial temperature
P2 = final pressure
T2 = final temperature
Let's plug in the given values into the equation:
P1 = 13 atm (initial pressure)
T1 = 25 °C (initial temperature)
T2 = 79 °C (final temperature)
Now let's solve for P2:
P1/T1 = P2/T2
13 atm / 25 °C = P2 / 79 °C
To get rid of the units, we can convert °C to Kelvin (K):
25 °C + 273.15 = 298.15 K
79 °C + 273.15 = 352.15 K
Now let's substitute the values:
13 atm / 298.15 K = P2 / 352.15 K
To solve for P2, we can cross multiply:
(13 atm) * (352.15 K) = (298.15 K) * P2
P2 = (13 atm * 352.15 K) / 298.15 K
P2 ≈ 15.36 atm
Therefore, the final pressure, when the fire extinguisher is used at a temperature of 79 °C, is approximately 15.36 atm.
To find the final pressure of the fire extinguisher when used at a temperature of 79°C, we can use the ideal gas law equation:
PV = nRT
Where:
P is the pressure
V is the volume
n is the number of moles
R is the ideal gas constant (0.0821 L·atm/(mol·K))
T is the temperature in Kelvin (K)
To solve the problem, we are given that V and n do not change. Therefore, we can consider them constant.
Given:
Initial pressure (P1) = 13 atm
Initial temperature (T1) = 25°C
Final temperature (T2) = 79°C
First, we need to convert the temperatures to Kelvin:
T1 = 25°C + 273.15 = 298.15 K
T2 = 79°C + 273.15 = 352.15 K
Now we can use the initial and final temperatures to calculate the initial and final pressures using the ideal gas law equation.
For the initial conditions (P1, T1):
P1V = nRT1
For the final conditions (P2, T2):
P2V = nRT2
As V and n do not change, we can divide the equations to eliminate these variables:
(P2V)/(P1V) = (nRT2)/(nRT1)
Simplifying the equation:
P2/P1 = T2/T1
Now we can substitute the values:
P2/13 atm = 352.15 K / 298.15 K
To solve for P2, rearrange the equation:
P2 = (13 atm) * (352.15 K / 298.15 K)
Calculating P2:
P2 ≈ (13 * 352.15) / 298.15 ≈ 15.36 atm
Therefore, the final pressure of the fire extinguisher when used at a temperature of 79°C, with V and n constant, is approximately 15.36 atm.