Bart
An efficient tax is one with a very low cost to administer vs. the revenue collected. An example would be a fuel tax collected at the gas pump.
An inefficient tax is one that has a high cost of government administration in proportion to the revenue collected. The tax concept that you advocate would seem to have a very high administrative cost. There would be a significant number of government officials involved in establishment of the precise amount of the tax to be levied on individual products as well as a high long term cost in government officials having to verify/validate the amount of CO2 emitted by different taxpayers. In addition, there is no data regarding the relative elasticity of the items that require the emissions of CO2 for their production so there is no guarantee that consumption would be reduced proportionally to revenues collected. As an example, would your tax which would raise the cost of cement reduce the demand?
Your proposed tax approach only makes any sense if it reduced demand for the products that require CO2 emissions for their production.