[TommyAtkins]

This is a problem from my summer assignment packet that I do not understand.

Copper wire is reacted with concentrated nitric acid and a brown gas is produced. Find the molar mass of the gas. Then find the unknown gas.

I know that you can probably already tell which gas it is from the first sentence, but I want to find the correct answer mathematically.

Measurements:

0.475 g of unknown gas in 250 mL flask
25 Celsius room temperature
757 mmHg pressure

I used the ideal gas law which is PV=nRT to solve for n. I got 10 for n which makes no sense.

If 0.475 grams of this gas is already 10 moles it makes no sense. The molar mass of a gas cannot be under 1. I am making a mistake here and I know it has something to do with the (0.475g) mass measurement they give me. Its throwing me off. I don't know how to use a measurement of mass in an equation that does not have a spot for mass, only volume.

Please tell me if this is a simple mathematical error I am making with the equation or if this is something else. I don't believe this is a simple math error. I think there is something I am supposed to do with the 0.475 grams they give me, I'm just not sure what it is. Its right under my nose and I can't figure it out.

[Borek]

n is definitely not 10, but it is impossible to say what your mistake is without seeing your calculations. I guess you used R with wrong units, or you forgot to convert mL of gas to L of gas (which is actually the same problem, R can be expressed using both mL and L for volume).

[TommyAtkins]

Understood. I am doing the problem correctly but must be using the wrong units of r or somewhere my math is wrong.

I think I know what my mistake is. R is 62.3 because it is mmHg. However, my volume units must be converted to .25 liters. Correct? I used 250 in my calculation.

Should I convert all units of volume to liters for future problems just to make things simple?

[sjb]

Understood. I am doing the problem correctly but must be using the wrong units of r or somewhere my math is wrong.

I think I know what my mistake is. R is 62.3 because it is mmHg. However, my volume units must be converted to .25 liters. Correct? I used 250 in my calculation.

Should I convert all units of volume to liters for future problems just to make things simple?

Looking through https://en.wikipedia.org/w/index.php?title=Gas_constant&oldid=675431338 I would suggest the answer to your first question is yes. What were the units of your R? As to question 2, that's up to you, perhaps at this early stage it would make sense, together with conversion of pressure to Pa, and temperature to kelvin.

[Borek]

I think I know what my mistake is. R is 62.3 because it is mmHg. However, my volume units must be converted to .25 liters. Correct? I used 250 in my calculation.

Your result was almost exactly 1000 times off, which is why I suspected mL/L problem.

Should I convert all units of volume to liters for future problems just to make things simple?

As sjb wrote - up to you. Personally I remember just the basic R value of 8.31 in SI units, and I know how to convert common pressure/temperature/volume units to those SI based (so the volume is in m³). This way I can deal with most problems. But sometimes I just check in the wikipedia what is the R value in some more exotic combination of units to not waste time on additional conversions. Works both ways, sometimes it is faster one way, sometimes the other.

[Enthalpy]

Should I convert all units of volume to liters for future problems just to make things simple?

Difficult decision...

My personal choice (having made other choices before) is SI units, plain and vanilla, everywhere and for every profession. At least they're consistent and exist for every job. Their drawback is that complete professions use other units (grams in chemistry, cm³ in microelectronics...) so one has to be vigilant at every data. Be prepared: this is not the last time you'll get trouble with units, it's daily life.

The incentive for SI came as I made mechanical engineering. There the length unit is mm, the force has been daN (then stress and stiffness moduli were in myriapieze) but shifted meanwhile to N, with stress and moduli in MPa. But as I wanted to compute resonant frequencies, the mm & MPa system collapsed, without a simple path to seconds and hertz. Though, I did need both resistances and frequencies - and SI offered this compatibility. The hard adaptation was worth it.

Units are a huge source of errors in any system. Besides being aware of them, you should have a few figures in memory for double-checking. In the present case, some 0.024m³ per mole of gas under usual conditions, so 10 mol in <1L shall raise an alarm. Knowing a few hundred figures suffices for varied professions.

Whatever your job and unit system, you must live with other units, so you need a unit converter.
https://joshmadison.com/convert-for-windows/ (English)
or "SI-Konverter" (German and English)
and certainly more.