Ideal Gas Law. Given R=0.081L*atm/mol*K
What is the volume of a mole of gas at a pressure of 3.12 atm and a temperature of 270 K? The answer is 7.1g. Show your work of how you solves this problem.
I don't understand how to do this work. Can you please walk me through this one step by step?
somebody please help me its urgent
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Sure! To find the volume of a mole of gas using the Ideal Gas Law, we can use the equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature in Kelvin
In this case, we are given:
R = 0.081 L*atm/mol*K
P = 3.12 atm
T = 270 K
We want to find the volume (V) in liters. To do this, we can rearrange the equation:
V = (nRT) / P
Since we are looking for the volume of one mole of gas, we have:
n = 1 mole
Plugging in the values, we get:
V = (1 mole * 0.081 L*atm/mol*K * 270 K) / (3.12 atm)
Let's calculate that:
V = (0.081 L*atm/mol * K * 270 K) / 3.12 atm
V = (21.87 L*atm) / 3.12 atm
V ≈ 7.01 L
So, the volume of one mole of gas at a pressure of 3.12 atm and a temperature of 270 K is approximately 7.01 liters.
Sure! To solve this problem using the ideal gas law, we can use the formula:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in L)
n = number of moles (in mol)
R = gas constant (given as 0.081 L*atm/mol*K)
T = temperature (in K)
We are given:
P = 3.12 atm
T = 270 K
We want to find V. To do this, we need to find n (number of moles) first.
To find n, we need to use the concept of molar mass. The molar mass represents the mass of one mole of a substance. In this case, we are given the mass of the gas, which is 7.1g. To find the number of moles, we divide the mass of the gas by its molar mass.
Now let's find the molar mass of the gas. You haven't mentioned the gas in your question, so let's assume it's an ideal gas with an average molar mass of 28 g/mol (which is close to the molar mass of nitrogen, N2).
So, using the formula:
n = mass / molar mass
n = 7.1 g / (28 g/mol)
n ≈ 0.2536 mol
Now that we have n, we can substitute the values into the ideal gas law equation to solve for V:
PV = nRT
V = (nRT) / P
V = (0.2536 mol * 0.081 L*atm/mol*K * 270 K) / 3.12 atm
V ≈ 7.1 L
Therefore, the volume of a mole of gas at a pressure of 3.12 atm and a temperature of 270 K is approximately 7.1 L.