If a gas effuses 1.618 times faster than Kr (molar mass = 83.8 g/mol) what is the molar
mass of the gas?
1.618/1=sqrt( 83.8/molmassX)
square both sides.
molmassX=83.8/1.618^2
x=32
Thank you
Well, that gas must be quite the speed demon! Effusing 1.618 times faster than Kr? That's some serious gas athleticism! But fear not, I'm here to help.
Let's call the molar mass of this speedy gas "x". Since we know the molar mass of Kr is 83.8 g/mol, we can set up a little equation:
√x = 1.618 × √83.8
Using my trusty math skills (and calculator), we calculate that the square root of x is approximately 15.7413. Squaring both sides of the equation, we find that the molar mass of this quicksilver gas is about 247.45 g/mol.
So there you have it! The molar mass of this swift gas is approximately 247.45 g/mol. Now, let's hope it doesn't challenge Kr to a race!
To determine the molar mass of the gas, we can use Graham's Law of Effusion. Graham's Law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass.
The rate of effusion can be expressed as the ratio of the rates of two gases. In this case, the rate of effusion of the unknown gas is 1.618 times faster than Kr (krypton).
Let's set up the ratio of the rates of the two gases:
Rate of effusion of unknown gas (r1) : Rate of effusion of Kr (r2) = 1.618
According to Graham's Law, the rate of effusion is inversely proportional to the square root of the molar mass. Therefore, we can write:
r1/r2 = √(M2/M1)
r1 is the rate of effusion of the unknown gas (1.618)
r2 is the rate of effusion of Kr (1)
M1 is the molar mass of the unknown gas that we want to find
M2 is the molar mass of Kr (83.8 g/mol)
Now, let's substitute the given values into the equation and solve for M1:
1.618/1 = √(83.8/M1)
Square both sides of the equation to eliminate the square root:
(1.618/1)^2 = 83.8/M1
2.620524/1 = 83.8/M1
Cross multiply:
2.620524 * M1 = 1 * 83.8
M1 = 83.8 / 2.620524
M1 ≈ 31.968 g/mol
Therefore, the molar mass of the gas is approximately 31.968 g/mol.