A 10.3g sample of an elemental gas has a volume of 58.4L at 758torr when the temperature is 2.5 C. Determine the identity of the gas.

we are close to STP here where one mol is 22.4 liters

58.4/22.4 is
around 2.61 moles
10.3/2.61 = 3.95 grams/mol
Helium maybe ?

Damon's estimate is quite good (and reasonable) and the answer is correct. If you want to do it without assuming it is 22.4 L/mol, it is done this way.

Use PV = nRT and solve for n = number of mols of the gas.
(758*58.4)/(760*0.08206*275.6) = 0.257 = n.
Then mols = grams/molar mass or
molar mass = g/mol = 10.3/0.257 = 4.01. Indeed that is He.

To determine the identity of the gas, we need to use the ideal gas law, which states:

PV = nRT

Where:
P is the pressure in atm
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

First, let's convert the given values to the appropriate units:

Pressure: 758 torr = 758/760 atm (since 1 atm = 760 torr) = 0.997 atm

Volume: 58.4 L (already in liters)

Temperature: 2.5 °C = 2.5 + 273.15 K = 275.65 K

Now, let's plug in the values into the ideal gas law equation and solve for the number of moles (n):

n = PV / RT

n = (0.997 atm) * (58.4 L) / (0.0821 L·atm/(mol·K) * 275.65 K)

n = 0.99893 mol

Since we are dealing with an elemental gas, the molar mass of the gas can be determined by dividing the mass of the sample by the number of moles:

molar mass = mass / number of moles

molar mass = 10.3 g / 0.99893 mol

molar mass = 10.31 g/mol

By comparing the molar mass value to the known molar masses of elements, we can determine the identity of the gas.

To determine the identity of the gas, we need to use the ideal gas law equation, which is:

PV = nRT

Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature

First, let's convert the given values to SI units:
- The pressure is given as 758 torr. To convert it to SI units (Pascal), we multiply by the conversion factor: 1 atm = 101325 Pa and 1 torr = 1/760 atm.
So, 758 torr is equal to (758/760) atm or 0.997 atm.

- The volume is given as 58.4 L.

- The temperature is given as 2.5 °C. To convert it to Kelvin, we add 273.15.
So, the temperature is 2.5 + 273.15 = 275.65 K.

Now, let's rearrange the ideal gas law equation to solve for the number of moles (n):

n = (PV) / (RT)

Plugging in the values into the equation:
n = (0.997 atm * 58.4 L) / ((0.0821 L * atm / K * mol) * 275.65 K)

Simplifying the equation:
n ≈ 1.81 moles

Now, we know that 10.3 grams of the elemental gas correspond to 1.81 moles. To determine the molar mass of the gas, we can use the formula:

Molar mass (g/mol) = mass (g) / moles

Plugging in the values into the formula:
Molar mass ≈ 10.3 g / 1.81 moles

Calculating the molar mass:
Molar mass ≈ 5.69 g/mol

By comparing the calculated molar mass to the molar masses of known elements, we can determine the identity of the gas. In this case, the molar mass (5.69 g/mol) is closest to chlorine (Cl), which has a molar mass of 35.45 g/mol.

Therefore, the gas is most likely chlorine (Cl).