# calculate the density of each of the following gases:

a)NH3 at 25 Degrees Celsius and 1.2 atm
b)Ar at 75 Degrees Celsius and 745 torr

## To calculate the density of a gas, we can use the ideal gas law, which states:

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 in Kelvin

To find the density (ρ) of a gas, we can rearrange the ideal gas law as:

ρ = (PM) / RT

Where:
ρ = density of the gas
P = pressure of the gas
M = molar mass of the gas
R = ideal gas constant
T = temperature in Kelvin

a) NH3 at 25 Degrees Celsius and 1.2 atm:
To find the molar mass of NH3:
M(N) = 14.01 g/mol
M(H) = 1.01 g/mol
M(NH3) = M(N) + (3 × M(H)) = 14.01 + (3 × 1.01) = 17.03 g/mol

To convert the temperature to Kelvin, we add 273.15 to the Celsius temperature:
T = 25 + 273.15 = 298.15 K

Using the formula, we can calculate the density:
ρ = (P × M) / (R × T)
ρ = (1.2 atm × 17.03 g/mol) / (0.0821 L·atm/(mol·K) × 298.15 K)
ρ ≈ 0.777 g/L

b) Ar at 75 Degrees Celsius and 745 torr:
To convert the temperature to Kelvin, we add 273.15 to the Celsius temperature:
T = 75 + 273.15 = 348.15 K

To convert the pressure from torr to atm, we divide by 760:
P = 745 torr / 760 torr/atm ≈ 0.9789 atm

To find the molar mass of Ar:
M(Ar) = 39.95 g/mol

Using the formula, we can calculate the density:
ρ = (P × M) / (R × T)
ρ = (0.9789 atm × 39.95 g/mol) / (0.0821 L·atm/(mol·K) × 348.15 K)
ρ ≈ 1.786 g/L

So, the calculated densities are:
a) NH3 at 25 Degrees Celsius and 1.2 atm, ρ ≈ 0.777 g/L
b) Ar at 75 Degrees Celsius and 745 torr, ρ ≈ 1.786 g/L

## To calculate the density of a gas, you need to use the ideal gas law, which relates the pressure, volume, and temperature of a gas. The formula for the ideal gas law is:

PV = nRT

where:
- P is the pressure of the gas (in atmospheres or torr)
- V is the volume of the gas (in liters)
- n is the number of moles of the gas
- R is the ideal gas constant (0.0821 L⋅atm/(mol⋅K) or 62.36 L⋅torr/(mol⋅K))
- T is the temperature of the gas (in Kelvin)

To calculate the density of a gas, you need to rearrange the ideal gas law equation as follows:

density = (molar mass * P) / (R * T)

where:
- molar mass is the mass of one mole of the gas (in g/mol)
- P is the pressure of the gas (in atm or torr)
- R is the ideal gas constant (in L⋅atm/(mol⋅K) or L⋅torr/(mol⋅K))
- T is the temperature of the gas (in Kelvin)

Now let's calculate the density of each gas:

a) NH3 at 25 degrees Celsius and 1.2 atm:
- Convert the temperature from Celsius to Kelvin:
T = 25 + 273.15 = 298.15 K

- The molar mass of NH3 is:
Molar mass of N = 14.01 g/mol
Molar mass of H = 1.01 g/mol
Molar mass of 3H = 3.03 g/mol
Total molar mass of NH3 = 17.04 g/mol

- Next, plug the given values into the density formula:
density = (molar mass * P) / (R * T)
density = (17.04 g/mol * 1.2 atm) / (0.0821 L⋅atm/(mol⋅K) * 298.15 K)

b) Ar at 75 degrees Celsius and 745 torr:
- Convert the temperature from Celsius to Kelvin:
T = 75 + 273.15 = 348.15 K

- The molar mass of Ar is:
Molar mass of Ar = 39.95 g/mol

- Next, convert the pressure from torr to atm:
745 torr = 745/760 atm = 0.9796053 atm

- Plug the given values into the density formula:
density = (molar mass * P) / (R * T)
density = (39.95 g/mol * 0.9796053 atm) / (0.0821 L⋅atm/(mol⋅K) * 348.15 K)