Question

Question #36ab0

Answer 1

I got `1.57` `"mol"`

Explanation:

I see what you did, you forgot to convert from `"kPa"` to `"atm"`.

You set up your equation correctly, but remember that when using the ideal-gas equation, your units must be the same as those in the units for `R`. Therefore, your units should be `"L"`, `"atm"`, `"mol"`, and `"K"`.

Let's convert from `"kPa"` to `"atm"`:

`160` `cancel("kPa")((1"atm")/(101.325cancel("kPa"))) = 1.58` `"atm"`

Since the temperature conversion was done correctly, I won't perform it here ( to Kelvin). The correct form is

`n = ((1.58cancel("atm"))(42.6cancel("L")))/((0.08206cancel(("L" · cancel("atm"))/("mol" · cancel("K"))))(523cancel("K"))) = color(red)(1.57` `color(red)("mol"`

Answer 2

Your error is probably in unit conversion.

`n = 1.57 color(white)"." "mol"`

Explanation:

The value of the ideal gas constant is `R = 0.0821 (L*"atm")/("mol"*K)`.

Therefore, to use the value 0.0821 in this problem, you must convert pressure to atmospheres, volume to liters, quantity to moles, and temperature to Kelvins.

Volume is in the correct units, and we are solving for moles so we don't need to "convert". So, we need to change pressure to `"atm"` and temperature to `K`.

`160 color(white)".""kPa" * (0.00987 color(white)".""atm")/"kPa" = 1.58 color(white)"." "atm"`

`250^@"C"+273 = 523 color(white)"." K`

Now we can solve the problem using the correct units:

`PV = nRT`

`(1.58color(white)".""atm")(42.6 color(white)"." L) = n(0.0821(L*"atm")/("mol"*K))(523color(white)"."K)`

`n = (1.58*42.6)/(0.0821*523) color(white)".""mol"`

`n = 1.57 color(white)"." "mol"`

Final Answer