A gas in a closed container has a pressure of 1.20 atm at a temperature of 308 K. If the pressure in the container is increased to 2.10 atm, what is the new temperature?
Use the sample problem below and follow the 5 steps to help you solve the problem you were given.
a
539 K
b
370 K
c
176 K
d
122 K
To solve this problem using the 5 steps, we can use the combined gas law equation, which is:
(P1 x V1) / (T1) = (P2 x V2) / (T2)
Step 1: Write down the known values
P1 = 1.20 atm
T1 = 308 K
P2 = 2.10 atm
Step 2: Determine the unknown value you need to find
We need to find T2, the new temperature.
Step 3: Rearrange the equation to solve for the unknown value
(T2) = (P2 x V2 x T1) / (P1 x V1)
Step 4: Substitute the known values into the rearranged equation
(T2) = (2.10 atm x T1) / (1.20 atm)
Step 5: Calculate the unknown value
(T2) = (2.10 atm x 308 K) / (1.20 atm)
(T2) = 539 K
Therefore, the new temperature is 539 K. The correct answer is a) 539 K.
To solve this problem, we can use the ideal gas law, which states that the product of pressure and volume is proportional to the product of the number of moles of gas and the temperature.
Step 1: Identify known values
Given:
Initial pressure (P1) = 1.20 atm
Initial temperature (T1) = 308 K
Final pressure (P2) = 2.10 atm
Step 2: Convert units (if necessary)
No unit conversions are required in this problem as all given values are already in the appropriate units.
Step 3: Apply the ideal gas law equation
The ideal gas law equation is given by:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
Since the volume and number of moles of gas are not given and are assumed to be constant in a closed container, we can write the equation as:
(P1/T1) = (P2/T2)
Step 4: Rearrange the equation to solve for T2
To solve for T2, we need to rearrange the equation as follows:
T2 = (P2 * T1) / P1
Step 5: Plug in the values and calculate
Now we can substitute the given values into the equation:
T2 = (2.10 atm * 308 K) / 1.20 atm
Using a calculator, we can calculate T2:
T2 ≈ 539 K
So, the new temperature in the container is approximately 539 K.
Therefore, the correct answer is option a) 539 K.
To solve this problem, we can use the combined gas law equation:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 = initial pressure
V1 = initial volume (assumed constant)
T1 = initial temperature
P2 = final pressure
V2 = final volume (assumed constant)
T2 = final temperature (unknown)
Step 1: Identify the known values:
P1 = 1.20 atm
T1 = 308 K
P2 = 2.10 atm
Step 2: Plug in the known values into the combined gas law equation:
(1.20 atm * V1) / (308 K) = (2.10 atm * V2) / (T2)
Step 3: Simplify the equation:
1.20 atm * V1 * T2 = 2.10 atm * V2 * 308 K
Step 4: Divide both sides of the equation by 1.20 atm * V1:
T2 = (2.10 atm * V2 * 308 K) / (1.20 atm * V1)
Step 5: Cancel out the units and calculate the value:
T2 = (2.10 * 308 K) / 1.20
T2 = 539 K
Therefore, the new temperature is 539 K.