Question

Part A;

The equation for molarity, M, is

M=n/V

where V is volume and n is the number of moles of solute.

A certain solution has a molarity of M = 2.73 mol/L and has a volume of V = 0.650 L . What is the value of n?

Express your answer numerically in moles.

part B;

The equation for photon energy, E, is

E=hcλ

where h = 6.626×10−34 J⋅s (Planck's constant) and c = 2.99×108 m/s (the speed of light).

What is the wavelength, λ, of a photon that has an energy of E = 3.98×10−19 J ?

Express your answer numerically in meters.

part C;

The ideal gas equation is

PV=nRT

where P is pressure, V is volume, n is the number of moles, R is a constant, and T is temperature.

You are told that a sample of gas has a pressure of P = 899 torr , a volume of V = 3280 mL, and a temperature of T = 307 K . If you use R = 8.206×10−2 L⋅atm/(K⋅mol) , which of the following conversions would be necessary before you could find the number of moles of gas, n, in this sample?

Check all that apply.

View Available Hint(s)

Check all that apply.

Convert the pressure to atmospheres (atm).
Convert the pressure to pascals (Pa).
Convert the volume to cubic meters (m3).
Convert the volume to liters (L).
Convert the temperature to degrees Celsius (∘C).
Convert the temperature to degrees Fahrenheit (∘F).

Answer 1

Part A : n = 1.77 moles

Part B : λ =
`2.01*10^(6) m^(-1)`

Part C : n = 0.154 moles

Step-by-step explanation:

Part A

The problem gives you the equation for molarity M:

`M=(n)/(V)`

n is the number of moles of solute and V is the volume

Then the problem gives you the molarity of a substance
`M=2.73(mol)/(L)` and the volume V = 0.650L, so you need to solve the equation for n:

`M=(n)/(V)`

as the V is dividing it passes to multiply the M:

n = M*V

and you should replace the values:

`n = 2.73(mol)/(L)*0.650L`

n = 1.77 moles

Part B

This time you have to solve the equation E = hcλ for λ that is the unknown information, so you have:

E = hcλ

h and c are multiplying so they pass to divide the E:

λ =
`(E)/(hc)`

and replacing the values:

λ =
`(3.98*10^(-19)J)/((6.626*10^(-34)J.s)(2.99*10^(8)(m)/(s)))`

λ =
`2.01*10^(6) m^(-1)`

PartC

In this part the problem gives you the equation PV=nRT and the first thing you should do is to verify that all the quantities are in consistent units so:

`R=8.206*10^(-2) (L.atm)/(K.mol)` so you need to convert the pressure to atmospheres and convert the volume to liters.

- Convert the pressure to atmospheres:

`P=899torr*(0.00131579atm)/(1torr)`

P = 1.18 atm

- Convert the volume to liters:

`V=3280mL*(1L)/(1000mL)`

V = 3.28L

To find the number of moles n, you should solve the equation for n:

Pv = nRT

As R and T are multiplying the n, they pass to divide to the other side of the equation:

`n=(PV)/(RT)`

And finally you should replace the values:

`n=((1.18atm)(3.28L))/((8.206*10^(-2)(L.atm)/(K.mol))(307K))`

n = 0.154 moles