An elemental gas has a mass of 10.3 g. If the volume is 58.4 L and the pressure is 758 torre at a temperature of 2.5 degrees C, what is the gas?
Use PV = nRT to solve for n = mols, then
n = mols = grams/molar mass
You know n and grams, solve for molar mass, then identify from that. I think you can use the periodic chart for that.
He(Helium)
use this formula N=PV/RT, then substitute the given quantities. Where, N=m(mass)/M(Molecular Mass).
Solution and Answer
n= 0.9973684211atm(58.4L)/0.0821(275.5K)
n= 2.575 mol.
Given: 10.3 g
10.3g÷2.575mol= 4 g/mol. Then look at your periodic table, where you can find the value of 4 g/mol in the element of He(Helium)
Well, well, well, looks like we have a mystery on our hands! Let me put on my detective hat and solve this case for you.
To determine the gas, we'll use the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.
First, let's convert the temperature from Celsius to Kelvin: 2.5 degrees C + 273.15 = 275.65 K. Detective Clue #1: We're looking for a substance with a temperature of 2.5 degrees Celsius.
Now, rearranging the ideal gas law equation to solve for n (the number of moles), we have: n = PV / RT. Plugging in the given values: n = (758 torr * 58.4 L) / (0.0821 L · atm/(K · mol) * 275.65 K). Detective Clue #2: We're dealing with pressure in torr, volume in liters, and temperature in Kelvin.
Calculating this, we find that n is approximately 19.70 moles.
Finally, we'll use the periodic table to figure out which element(s) have a molar mass of approximately 10.3 grams divided by 19.70 moles.
Drumroll, please...
And the answer is... Neon! (Symbol: Ne)
Congratulations, we've cracked the case!
To determine the gas, we can use the ideal gas law equation, which is represented as:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
First, let's convert the given units to those that are commonly used in the ideal gas law equation.
The pressure is given as 758 torr. We know that 1 torr is equal to 1 mmHg, and the standard unit in the ideal gas law is Pascal (Pa). To convert torr to Pa, we multiply by the conversion factor:
1 torr = 1 mmHg = 133.32 Pa
So, the pressure in pascals is:
758 torr * (133.32 Pa / 1 torr) = 101196.56 Pa
The volume is given as 58.4 L, which is already in the required unit, so no conversion is necessary.
The temperature is given as 2.5 degrees Celsius. However, the ideal gas law requires temperature to be in Kelvin (K). To convert Celsius to Kelvin, we add 273.15:
T(K) = T(°C) + 273.15
T(K) = 2.5°C + 273.15 = 275.65 K
Now, we have the values we need to solve the ideal gas law equation, except for the number of moles (n). The number of moles can be determined using the following equation:
n = m / M
Where:
n = number of moles
m = mass of the gas
M = molar mass of the gas
Given that the gas has a mass of 10.3 g, we need to find the molar mass of the gas in order to calculate the number of moles. To do this, we'll need to know the identity of the gas.
Without knowing the specific gas, it is challenging to calculate the molar mass and, consequently, the number of moles. If you have additional information about the gas, such as its molecular formula or specific properties, I can assist you further in determining the identity of the gas.