Calculate the mass of 30.0 L of NH3 at 37° C and 900. mm Hg. Show calculation solutions.
Use PV = nRT and solve for n = number of moles.
Then moles = n = grams/molar mass. You know n and molar mass (17), solve for grams
Well, well, well, we've got ourselves a chemistry question, don't we? Alright, let's put on our lab coats and dive into it!
To calculate the mass of a gas, we'll need to use the ideal gas law, which states:
PV = nRT
Where:
- P is the pressure (in atm or Pa, not mm Hg - but no worries, I'll convert it for you).
- V is the volume (in liters).
- n is the number of moles.
- R is the ideal gas constant (0.0821 L·atm/mol·K).
- T is the temperature (in Kelvin).
Now, let's convert those pesky units to get on the same page. First off, we'll convert the pressure from 900. mm Hg to atm. Divide 900 by 760, and you get approximately 1.184 atm.
The temperature needs to be in Kelvin, so we'll add 273 to 37°C, giving us 310 K. Got it so far?
Next, we'll rearrange the ideal gas law equation to solve for moles:
n = (PV) / (RT)
Plugging in the numbers, we have:
n = (1.184 atm * 30.0 L) / (0.0821 L·atm/mol·K * 310 K)
Now, let's crunch the numbers!
n ≈ 0.1446 moles
Finally, the mass can be calculated using the molar mass of ammonia (NH3), which is about 17 g/mol.
mass = n * molar mass
mass ≈ 0.1446 moles * 17 g/mol
And the grand total is...
mass ≈ 2.46 grams
Tada! There you go, my friend. Approximately 2.46 grams of humorously calculated NH3!
To calculate the mass of NH3, we need to 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 Kelvin)
First, let's convert the given values to the appropriate units:
37 °C = 273 + 37 = 310 K (temperature in Kelvin)
900 mm Hg = 900 / 760 = 1.18 atm (pressure in atm)
Now, we can rearrange the ideal gas law equation to solve for moles (n):
n = PV / RT
Substituting the given values:
n = (1.18 atm)(30.0 L) / (0.0821 L·atm/mol·K)(310 K)
n = 0.1088 moles
Next, we need to calculate the molar mass of NH3. The molar mass of nitrogen (N) is 14.01 g/mol, and the molar mass of hydrogen (H) is 1.008 g/mol. Since ammonia (NH3) consists of one nitrogen atom and three hydrogen atoms, we can find the molar mass as:
Molar mass of NH3 = (1 mol N)(14.01 g/mol) + (3 mol H)(1.008 g/mol)
Molar mass of NH3 = 17.03 g/mol
Finally, we can calculate the mass of 30.0 L of NH3:
Mass of NH3 = n × molar mass
Mass of NH3 = 0.1088 mol × 17.03 g/mol
Mass of NH3 = 1.85 g
Therefore, the mass of 30.0 L of NH3 at 37°C and 900 mm Hg is approximately 1.85 grams.
To calculate the mass of a gas, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure of the gas (in atm)
V = volume of the gas (in L)
n = number of moles of the gas
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature of the gas (in Kelvin)
To solve this problem, we need to convert the given conditions to the appropriate units and then use this equation to calculate the number of moles (n). Finally, we can calculate the mass using the molar mass of NH3.
Step 1: Convert the temperature to Kelvin
The given temperature is 37° C. To convert it to Kelvin, we add 273.15 to the Celsius value:
T = 37 + 273.15 = 310.15 K
Step 2: Convert the pressure to atm
The given pressure is 900. mm Hg. To convert it to atm, we divide by the conversion factor of 760 mm Hg in 1 atm:
P = 900 mm Hg / 760 mm Hg/atm ≈ 1.18 atm
Step 3: Calculate the number of moles (n)
Using the ideal gas law equation, we can rearrange it to solve for n:
n = PV / RT
n = (1.18 atm) * (30.0 L) / (0.0821 L·atm/(mol·K)) * (310.15 K)
n ≈ 1.42 moles
Step 4: Calculate the mass
The molar mass of NH3 is calculated by adding the atomic masses of nitrogen (N) and hydrogen (H):
Molar mass of NH3 = 14.01 g/mol (N) + (1.01 g/mol * 3) (H)
Molar mass of NH3 ≈ 17.03 g/mol
To calculate the mass, we multiply the number of moles by the molar mass:
Mass = n * Molar mass
Mass = 1.42 moles * 17.03 g/mol
Mass ≈ 24.20 g
Therefore, the mass of 30.0 L of NH3 at 37° C and 900. mm Hg is approximately 24.20 grams.