if I want to find the uncertainty for a certain molar mass containing 4 atoms of Oxygen, do I multiply the error and the MM by 4: like this 4(15.9994 plus of minus .0003) = 63.9976 plus or minus .0012 (distribute the 4?)
or follow the rules for mult. of uncertainty which would be turning them into a percent, (.0003/15.9994 x 100) squaring the result, taking the square root and then do the mutiplication by 4? 63.9976 plus or minus .0075 % uncertainty?
To find the uncertainty in the molar mass containing 4 atoms of oxygen, you should follow the rules for multiplication of uncertainties. Here's the correct calculation:
1. Calculate the relative uncertainty for a single atom:
Relative uncertainty = (0.0003 / 15.9994) x 100 = 0.001875
2. Square the relative uncertainty:
Squared uncertainty = 0.001875^2 = 0.000003516
3. Take the square root of the squared uncertainty:
Square root of uncertainty = √0.000003516 = 0.001875
4. Multiply the uncertainty by 4 to account for 4 atoms of oxygen:
Total uncertainty = 0.001875 x 4 = 0.0075
Therefore, the uncertainty in the molar mass is 0.0075. As for the final value, you mentioned 63.9976, but the exact molar mass of 4 oxygen atoms is 63.9994 g/mol. So the molar mass would be written as 63.9994 plus or minus 0.0075 g/mol.
To find the uncertainty in the molar mass of a compound containing 4 atoms of Oxygen, you would multiply the error and the molar mass by 4. However, it is important to note that the error in molar mass should be expressed as a relative uncertainty or a percent uncertainty, rather than an absolute uncertainty.
To calculate the relative uncertainty or percent uncertainty, you would divide the error value by the molar mass value and then multiply by 100 to express it as a percentage.
In your example, if the error in molar mass is given as ±0.0003 and the molar mass of Oxygen is 15.9994, you would first calculate the relative uncertainty as follows:
(0.0003 / 15.9994) × 100 = 0.001875 %
Next, you would square the relative uncertainty and then take the square root to find the absolute uncertainty:
√(0.001875^2) = 0.0019
So, the absolute uncertainty in the molar mass of Oxygen is approximately ±0.0019.
Finally, you would multiply the absolute uncertainty by 4 to account for the 4 Oxygen atoms in your compound:
4 × 15.9994 ± 4 × 0.0019 = 63.9976 ± 0.0076
Therefore, the molar mass of the compound containing 4 atoms of Oxygen would be approximately 63.9976 g/mol with an uncertainty of ±0.0076 g/mol.