1. the molar mass of helium is 4.00 g/mol.

calculate the volume of 1 mol of helium at STP (T = 273, P = 1 atm)
what is the density of helium at STP?

2. the density of an ideal gas is 1.35 kg/m^3. if the temperature is Kelvin and the pressure are both doubled, find the new density of the gas.

well nobody is gonna help you with that attitude :-(

1)

V = nRT/P
= (1 x 8.314 x 273/101.23)
= 22.4 L

so the density is 4g/22.4L

2) assuming the volume is held constant, the density would be the same.

1. To calculate the volume of 1 mol of helium at STP (Standard Temperature and Pressure), we can use the Ideal Gas Law equation:

PV = nRT

Where:
P = pressure (1 atm)
V = volume (unknown)
n = number of moles (1 mol)
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature in Kelvin (273 K)

Rearranging the equation to solve for V:

V = (nRT) / P

Substituting the known values:

V = (1 mol)(0.0821 L·atm/mol·K)(273 K) / 1 atm
V = 22.42 L

Therefore, the volume of 1 mol of helium at STP is 22.42 L.

To calculate the density of helium at STP, we can use the formula:

Density = mass / volume

The molar mass of helium is given as 4.00 g/mol, so we can assume that 1 mol of helium has a mass of 4.00 g.

Substituting the known values:

Density = (4.00 g) / (22.42 L)

Converting units to the proper form:

Density = (4.00 g) / (0.02242 m^3)
Density = 178.3 g/m³

Therefore, the density of helium at STP is 178.3 g/m³.

2. To find the new density of a gas when the temperature and pressure are both doubled, we can use the ideal gas law equation PV = nRT.

We have the original density of the gas as 1.35 kg/m³. Since the density is mass divided by volume, we can assume that the mass of the gas is equal to the original density multiplied by the original volume.

Let's assume the original volume is V1.

Mass = density * volume = 1.35 kg/m³ * V1 = 1.35 V1 kg

When the temperature and pressure are both doubled, we know that the pressure P2 = 2P1 and the temperature T2 = 2T1.

Now, we'll use the ideal gas law equation to find the new volume V2.

(P2 * V2) / (nR * T2) = P1 * V1 / (nR * T1)

Since the number of moles (n), the gas constant (R), and the substance (gas) remain the same, we can simplify the equation:

(P2 * V2) / T2 = P1 * V1 / T1

Substituting the known values:

(2P1 * V2) / (2T1) = P1 * V1 / T1

Cancelling out the common terms, we get:

V2 = V1

Therefore, the new volume of the gas remains the same.

Since density = mass / volume, and the volume remains the same, the new density of the gas will also be 1.35 kg/m³.

1. To calculate the volume of 1 mol of helium at STP, we can 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 ideal gas constant, and T is the temperature.

At STP (Standard Temperature and Pressure), the temperature (T) is 273 K and the pressure (P) is 1 atm. We are given that the molar mass of helium is 4.00 g/mol.

Step 1: Convert molar mass to kilograms.
Molar mass of helium = 4.00 g/mol
1 mol of helium = 4.00 grams
1 kg = 1000 grams

So, molar mass of helium = 4.00 g/mol * (1 kg / 1000 g) = 0.00400 kg/mol

Step 2: Calculate the number of moles.
n = mass / molar mass
Since we have 1 mole of helium, the mass is equal to the molar mass:
n = 1 mol

Step 3: Substitute the values into the ideal gas law equation and solve for V.
PV = nRT
V = (nRT) / P

Plugging in the values:
V = (1 mol * 0.00400 kg/mol * 8.314 J/(mol·K) * 273 K) / 1 atm

Simplifying:
V = 0.931 L/mol

Therefore, the volume of 1 mol of helium at STP is approximately 0.931 liters.

Now, to calculate the density of helium at STP, we divide the mass by the volume:
Density = Mass / Volume

The mass of 1 mole of helium is equal to its molar mass, which we already calculated as 4.00 g/mol. Since 1 mole of helium has a mass of 4.00 grams, the density can be calculated as follows:

Density = Mass / Volume = 4.00 g / 0.931 L

Converting grams to kilograms:
Density = 4.00 g / 1000 g/kg / 0.931 L = 0.00430 kg/L

So, the density of helium at STP is approximately 0.00430 kg/L.

2. To find the new density of the gas when the temperature and pressure are both doubled, we can use the ideal gas law equation again.

The ideal gas law equation is 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.

Step 1: Calculate the initial density of the gas.
Given that the density of the gas is 1.35 kg/m^3, we can proceed as follows:

Density = Mass / Volume

The initial mass is not given, so we'll use the general formula: Mass = Density * Volume.

Let's assume the initial volume to be V1.

So, the initial mass = Density * V1.

Step 2: Double the pressure and temperature.
Given that the pressure and temperature are both doubled, we multiply the initial pressure (P1) and initial temperature (T1) by a factor of 2.

P2 = 2 * P1 (new pressure)
T2 = 2 * T1 (new temperature)

Step 3: Use the ideal gas law equation to find the final volume (V2).
V1 is the initial volume and V2 is the final volume.

P1 * V1 = nRT1 (initial state)
P2 * V2 = nRT2 (final state)

Since the number of moles (n) and the gas constant (R) remain constant, we can rewrite the equations as:
P1 * V1 = constant
P2 * V2 = constant

Taking the ratio of the two equations:
(P1 * V1) / (P2 * V2) = V1 / V2

Simplifying:
V2 = (P2 * V1) / P1

Step 4: Calculate the final mass (M2).
Similar to step 1, we can use: M2 = Density2 * V2.

Step 5: Calculate the final density (Density2).
Density2 = M2 / V2

Putting it all together:
Density2 = (Density * V1) / [(P2 * V1) / P1]

Density2 = Density * (P1 / P2)

Since P1 = 1 atm and P2 = 2 atm (because pressure was doubled), we have:
Density2 = Density * (1 / 2)

Substituting the given density of 1.35 kg/m^3, we have:
Density2 = 1.35 kg/m^3 * (1 / 2) = 0.675 kg/m^3

Therefore, the new density of the gas, when the temperature and pressure are both doubled, is approximately 0.675 kg/m^3.