Question

A bacterial culture isolated from sewage produces 0.376 L of methane (CH4) at 304 K and 1.5 atm. What would the volume of the methane be at STP?

A particular chemical reaction requires 295 mol sulfur dioxide gas (SO2) A scientist has a 5.2 L tank of SO2 gas at a pressure of 45.2 atm and a temperature of 293 K. Does the scientist have enough SO2 to carry out the reaction? If so, how many moles of SO2 will be left over? If not, how many more moles of SO2 does the scientist need? Explain your answer.

The maximum safe pressure that a 4.00 L vessel can hold is 3.50 atm. If the vessel contains 0.410 mol of helium, what if the maximum temperature to which the vessel can be subjected?

A 3.4 L rigid container holds a sample of argon (Ar) gas at a pressure of 1.0 atm and a temperature of 263 K. If a scientist adds 2.5 mol Ar to the container without changing the temperature or volume, what will the new pressure inside the container be? (Hint: First calculate the number of moles that were in the container originally)

Please help me, I don't really understand this.

Answer 1

1) we are going to use the ideal gas law to get n the number of moles :

when PV = nRT where:

P is the pressure = 1.5 atm but it should be in (Pa) so we are going to convert it

P = 1.5 atm *101325 = 151987.5 Pa = 151.9875 KP

and where: V is the volume = 0.376 L and

T is the temperature = 304 K

and R is the ideal gas constant = 8.314 J/K.mol

and n is the number of moles.

So, by substitution:

151.987.5 KPa* 0.376L = n * 8.314*304K .

∴ n = 0.0226 moles. at STP 1 mol of an ideal gas will occupy 22.4 L of volume.

So the volume which be occupied with 0.0226 moles is = 0.0226 moles * 22.4L =0.50624 L.

2) we are going to use the ideal gas formula also: PV=nRT

when P is the pressure = 45.2 atm * 101.325 KPa/atm = 4579.89KPa

& V is the volume = 5.2L

& R is the ideal gas constant = 8.314J/K.mol and

T = 293 K .

So by substitution: n = 4579.89 * 5.2 / 8.314 * 293 = 9.78 moles.

so, there is no enough SO2 & the moles needed is

= intial moles - n
= 295 mol - 9.78 mol
= 285.22 moles needed

3) we will use the ideal gas formula PV= nRT

where P is the pressure = 3.5*101.325 KPa/atm = 354.63KPa

& V is the volume = 4 L

and n is the moles number = 0.410 mol

,so by substitution:

T= P*V/n*R

= 354.63 * 4 L / 8.314*0.410

= 416 K

∴ the temperature is = 416 K

4) first we need to get the original n number of moles by using the ideal gas law , PV=nRT:

where P is the pressure = 1 atm * 101.325KPa = 101.325KPa

& v is the volume =3.4L

& R is the ideal gas constant = 8.314 J/K.mol

& T is the temperature = 263K

so by substitution:

we can get n:

n = PV/RT

= 101.325*3.4/8.314*263

= 0.157 mole

the new n = 0.157 + 2.5

= 2.657 moles

∴ the pressure P = 2.657*8.314*263/3.4L = 1708.74 KPa