A certain gas has a density of 1.053 g/L at 25C and 752 mmHg. What is the molar mass of this gas?

Assuming the gas is ideal, we use the formula

ρ = P*MM / RT
where
ρ = density (g/L)
P = pressure (atm)
MM = molar mass (g/mol)
R = gas constant = 0.0821 L-atm/mol-K
T = temperature (K)
Note that this formula is just derived from the ideal gas law (PV = nRT).
Convert the given units to the appropriate units, then substitute:
MM = ρRT / P
MM = 1.053 * 0.0821 * (25+273) / (752/760)
MM = 26.04 g/mol

Hope this helps~ :3

To find the molar mass of the gas, we need to use the Ideal Gas Law equation:

PV = nRT

Where:
P = pressure in atm,
V = volume in liters,
n = number of moles,
R = gas constant (0.0821 L.atm/mol.K),
T = temperature in Kelvin.

First, let's convert the given information into the appropriate units:
- Pressure: 752 mmHg can be converted to atm by dividing by 760 mmHg/atm:
Pressure (P) = 752 mmHg / 760 mmHg/atm = 0.9895 atm

- Temperature: 25°C needs to be converted to Kelvin by adding 273.15 to the Celsius value:
Temperature (T) = 25°C + 273.15 = 298.15 K

Now we can rearrange the Ideal Gas Law equation to solve for moles (n), since we have the values for P, V, R, and T:

n = PV / RT

Next, we need to calculate the moles (n) of the gas using the given information. However, we do not have the volume (V) of the gas. We can calculate it using the density (d) of the gas.

Density (d) = mass / volume

Rearranging the equation to solve for the volume (V):

V = mass / density

Given density = 1.053 g/L, we need to compute the mass of gas present in 1 L of the gas.

Now, using the relationship between moles, mass, and molar mass:
- Moles (n) = mass / molar mass
- Mass = density * volume = 1.053 g/L * 1 L = 1.053 g

Substituting the known values into the equation:

n = PV / RT = (0.9895 atm) * (1 L) / (0.0821 L.atm/mol.K * 298.15 K)

Simplifying the equation:

n = 0.04026 mol

Finally, we can solve for the molar mass (Molar mass = mass/moles):

Molar mass = 1.053 g / 0.04026 mol

Molar mass = 26.115 g/mol

Therefore, the molar mass of the gas is 26.115 g/mol.

To determine the molar mass of the gas, we need to use the ideal gas law equation, which relates the pressure, volume, molar mass, and temperature of a gas.

The ideal gas law equation is given as:

PV = nRT

Where:
P = pressure of the gas (in this case, 752 mmHg)
V = volume of the gas (in this case, 1 L)
n = number of moles of gas
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature of the gas (in this case, 25°C or 298 K)

Now, we can rearrange the ideal gas law equation to solve for the number of moles (n) of gas:

n = PV / RT

To calculate the number of moles, we need to convert the pressure from mmHg to atm and the temperature from Celsius to Kelvin.

1 atm = 760 mmHg (approx.)
So, we can convert 752 mmHg to atm by dividing it by 760:

752 mmHg / 760 mmHg/atm = 0.9895 atm

To convert the temperature from Celsius to Kelvin, we need to add 273.15 to the Celsius temperature:

25°C + 273.15 = 298.15 K

Now, we can substitute the values into the equation:

n = (0.9895 atm) * (1 L) / [(0.0821 L·atm/mol·K) * (298.15 K)]

Simplifying the equation:

n = 0.03981 mol

The number of moles (n) of gas is approximately 0.03981 mol.

To find the molar mass, we can use the formula:

Molar mass (g/mol) = Mass (g) / Moles (mol)

In this case, we know the density of the gas at 25°C is 1.053 g/L. The density is defined as mass per unit volume. So, the mass (m) of the gas is equal to the density times the volume:

Mass = density * volume

Mass = 1.053 g/L * 1 L = 1.053 g

Now, we can calculate the molar mass:

Molar mass = 1.053 g / 0.03981 mol

Molar mass ≈ 26.46 g/mol

Therefore, the molar mass of the gas is approximately 26.46 g/mol.