a 25.0 sample of nitrogen has a volume of 50.0L and a pressure of 630. mmHg. what is the temperature of the gas?
Use PV = nRT
T will be in kelvin.
To find the temperature of the gas, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
Given:
Pressure (P) = 630 mmHg
Volume (V) = 50.0 L
We need to calculate the number of moles (n) to use in the equation. For this, we'll use the formula:
n = mass / molar mass
The molar mass of nitrogen (N₂) is 28.01 g/mol.
Given:
Mass = 25.0 g
Molar mass = 28.01 g/mol
First, let's calculate the number of moles (n):
n = 25.0 g / 28.01 g/mol
n ≈ 0.892 mol
Now we can substitute the values into the ideal gas law equation and solve for temperature:
PV = nRT
630 mmHg * 50.0 L = 0.892 mol * R * T
Now, we need to convert the pressure from mmHg to atm since the ideal gas constant has the units atm•L/mol•K:
(630 mmHg / 760 mmHg/atm) * 50.0 L = 0.892 mol * R * T
(0.8295 atm) * 50.0 L = 0.892 mol * R * T
41.475 L*atm = 0.892 mol * R * T
Now we can rearrange the equation to solve for temperature (T):
T = (41.475 L*atm) / (0.892 mol * R)
The value of the ideal gas constant (R) is 0.0821 L*atm/(mol*K).
T = (41.475 L*atm) / (0.892 mol * 0.0821 L*atm/(mol*K))
T ≈ 622 K
Therefore, the temperature of the gas is approximately 622 K.
To solve this problem, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles of gas
R = ideal gas constant
T = temperature
First, let's convert the given pressure from mmHg to atm since the ideal gas constant is usually expressed in atm.
1 atm = 760 mmHg
So, the pressure in atm would be:
630 mmHg / 760 mmHg = 0.82895 atm (rounded to five decimal places)
Now, let's determine the number of moles of nitrogen using the ideal gas law equation.
Rearranging the equation, we get:
n = PV / RT
Substituting the given values:
n = (0.82895 atm) × (50.0 L) / ((0.0821 L·atm/mol·K) × T)
Simplifying:
n = 41.4475 / T
The volume is given in liters, so the gas constant R needs to be in units of L·atm/mol·K.
Now, let's solve for T. Multiply both sides of the equation by T:
nT = 41.4475
T = 41.4475 / n
We need to know the number of moles of nitrogen to calculate the temperature.
Do you have any information on the number of moles of nitrogen in the sample?