1.50 mol sample of helium at a certain pressure and temperature has a volume of 31.4 L. a second sample of helium at the same temperature and pressure has a volume of 42.4 L. Therefore the second sample contains how many moles of helium?

You can reason through it this way

PV = nRT. Since P, R and T are constant, then V = n*constant which I'll call k and
V = nk.
Evaluate k by 31.4 = 1.5k and k = 31.4/1.4 = 20.93.

Then V = nk
41.4 = n*20.93 and
n = 41.4/20.93 - 2.03 mols.

OR you can reason that a higher volume at the same T and P must have more moles by the fraction
1.5 x (41.4/31.4) = ?

To find the number of moles of helium in the second sample, we can use the concept of the ideal gas law.

The ideal gas law is given by the equation:
PV = nRT

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

Since the temperature and pressure are the same for both samples of helium, we can write:

P₁V₁ = n₁RT
P₂V₂ = n₂RT

Given:
n₁ = 1.50 mol
V₁ = 31.4 L
V₂ = 42.4 L

Using the equation P₁V₁ = n₁RT, we can solve for n₁:

n₁ = (P₁V₁) / (RT)

Similarly, using the equation P₂V₂ = n₂RT, we can solve for n₂:

n₂ = (P₂V₂) / (RT)

Since P₁ = P₂ and T₁ = T₂, we can simplify the equation to:

n₂ = (V₂ / V₁) * n₁

Substituting the given values into the equation, we get:

n₂ = (42.4 L / 31.4 L) * 1.50 mol

Calculating this expression, we find:

n₂ = 2.03 mol

Therefore, the second sample contains approximately 2.03 moles of helium.

To find the number of moles of helium in the second sample, we can use the concept of 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 ideal gas constant, and T is the temperature.

Given:
For the first sample: n1 = 1.50 mol, V1 = 31.4 L
For the second sample: V2 = 42.4 L (we need to find n2)

Since the temperature and pressure are the same for both samples, we can write the equation as:

P × V1 = n1 × R × T ---(equation 1)
P × V2 = n2 × R × T ---(equation 2)

Since equation 1 and equation 2 have the same pressure, temperature, and ideal gas constant, we can set them equal to each other:

n1 × R × T = n2 × R × T

Canceling out R and T from both sides:

n1 × V1 = n2 × V2

Now, substitute the known values:

1.50 mol × 31.4 L = n2 × 42.4 L

Solve for n2:

n2 = (1.50 mol × 31.4 L) / 42.4 L

n2 = 1.12 mol

Therefore, the second sample contains 1.12 moles of helium.