If 20.0g of nitrogen gas has a volume of 4.00L and a pressure of 6.0 atm, what is its temperature?
To determine the temperature of the nitrogen gas, you can use the Ideal Gas Law, which states that the product of pressure (P) and volume (V) of a gas is directly proportional to the number of moles (n) of the gas and its temperature (T), when the quantity of gas is held constant. The formula for the Ideal Gas Law is:
PV = nRT
Where:
P = pressure of the gas
V = volume of the gas
n = number of moles of the gas
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature of the gas (in Kelvin)
In this case, you are given:
P = 6.0 atm
V = 4.00 L
n = moles of nitrogen gas (not given)
R = 0.0821 L·atm/(mol·K)
To use the Ideal Gas Law, you need to determine the number of moles of nitrogen gas. To do this, you can use the molar mass of nitrogen:
Molar mass of nitrogen gas (N₂) = 28.0134 g/mol
Given that you have 20.0g of nitrogen gas, you can calculate the number of moles using the formula:
moles = mass / molar mass
moles = 20.0g / 28.0134 g/mol
Once you have the number of moles, you can rearrange the Ideal Gas Law equation to solve for the temperature (T):
T = (PV) / (nR)
Substituting the given values:
T = (6.0 atm * 4.00 L) / (moles * 0.0821 L·atm/(mol·K))
Calculate the moles of nitrogen gas using the molar mass, and substitute into the equation to find the temperature.