What is the pressure of 1.6 moles of a gas occupying 31.7 L at a temperature of 290 K?
Given R= 0.0821 L atm / mol K
Use the sample problem below and follow the 5 steps to help you solve the problem you were given.
a
14.6 atm
b
0.83 atm
c
0.14 atm
d
1.20 atm
To solve this problem, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in L)
n = number of moles
R = gas constant (0.0821 L atm / mol K)
T = temperature (in K)
Step 1: Identify the given values:
n = 1.6 moles
V = 31.7 L
T = 290 K
R = 0.0821 L atm / mol K
Step 2: Plug in the values into the ideal gas law equation:
PV = nRT
P * 31.7 = 1.6 * 0.0821 * 290
Step 3: Solve for P:
P = (1.6 * 0.0821 * 290) / 31.7
Step 4: Calculate the value of P:
P = 1.465 atm
Step 5: Round the answer to the appropriate number of significant figures:
The pressure of 1.6 moles of gas occupying 31.7 L at a temperature of 290 K is approximately 1.47 atm.
Therefore, the correct answer is (a) 1.47 atm.
To find the pressure of the gas, we can use the ideal gas law equation:
PV = nRT
Where:
P is the pressure of the gas
V is the volume of the gas
n is the number of moles of the gas
R is the gas constant
T is the temperature in kelvin
In this case, we are given:
n = 1.6 moles
V = 31.7 L
R = 0.0821 L atm / mol K
T = 290 K
To solve for P, we can rearrange the equation as:
P = (nRT) / V
Substituting the given values:
P = (1.6 moles * 0.0821 L atm / mol K * 290 K) / 31.7 L
Simplifying:
P = 0.10237 atm
Therefore, the pressure of the gas is approximately 0.102 atm.
To find the pressure of a gas, we can use the Ideal Gas Law, which is represented by the equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
Step 1: Write down the given values:
Number of moles (n) = 1.6 moles
Volume (V) = 31.7 L
Temperature (T) = 290 K
Ideal Gas Constant (R) = 0.0821 L atm / mol K
Step 2: Plug in the values into the equation for the Ideal Gas Law:
PV = nRT
P * 31.7 L = 1.6 moles * 0.0821 L atm / mol K * 290 K
Step 3: Cancel out units and calculate:
P * 31.7 = 1.6 * 0.0821 * 290
P = (1.6 * 0.0821 * 290) / 31.7
P ≈ 1.147 atm
Step 4: Round the final answer to the appropriate number of significant figures:
P ≈ 1.15 atm
So, the pressure of the gas is approximately 1.15 atm.
Therefore, the correct answer is:
d. 1.20 atm