1. Maybe -20?
2. If so, about $10^{11}$ kg.
For question 1, I’m going to guess that changing the average temperature from 16 degrees Celcius to -20 degrees will cause enough havok to create mass extinctions. The average temperature during the last ice age was about 10 degrees. If the temperature near the equator ranges from 10-30 above the average, -20 globally would get the equatorial temperature dipping below freezing regularly.
For the hose-to-the-sky cooling scheme, I’m getting all of my information from <PERSON> and <PERSON>’s SuperFreakonomics. This is just a rough estimate, so hopefully that will be good enough.
Intellectual Venture’s plan to completely reverse global warming requires 5 base stations, located around the globe, each with 3 hoses (p. 196) spraying liquified sulfur dioxide into the stratosphere, 7 miles up (p. 189). Each hose sprays at 34 gal/min (p. 192), or 190 kg/min, so 2800 kg/min for all 15 hoses. Since they say this will “effectively reverse global warming” (p. 912
196), let’s assume that 2800 kg/min will decrease the average temperature of the earth by 2 degrees Celcius.
I’m guessing that sulfur dioxide injection would be affected by the law of diminishing returns, but I’m going to assume a linear relationship because I lack the skill to do anything else. With that assumption, decreasing the average global temperature 36 degrees would require pumping about 100,000 kg of sulfur dioxide per minute. To cause mass extinction, let’s say we have to run this for two years, to make sure that artic and antarctic animals don’t get a chance to stock up on more food in the “summer”. That will take $10^{11}$ kg of sulfur dioxide, or $5\times 10^{10}$ kg of sulfur (1 kg of sulfur yields 2 kg of sulfur dioxide). Do we have that much sulfur handy?
It looks like it. The Athabasca Oil Sands in Alberta, Canada have pyramids of sulfur as a waste product of oil extraction. The book describes pyramids “a hundred meters high by a thousand meters wide” (p. 195), or 30 million cubic meters = $6\times 10^{10}$ kg S in each pyramid.
How many hoses do our five pumping stations need? Each station needs to output 20,000 kg/min, which would require about 100 hoses at each site, or maybe bigger hoses.
If we assume just two giant pumping stations, at the Athabasca site and at a similar site somewhere in the southern hemisphere, the sulfur dioxide "stratoshield" would shade the earth's surface in about 10 days (P. 194). Each station has enough sulfur to run for at least two years, so together, they can freeze the earth for more than four years (assuming the earth cools off quickly once it can’t receive as much energy from the sun).
The sulfur dioxide would settle out of the atmosphere “within a few years” (p. 197).
If my arithmetic is correct, this scenario is too close to plausibility for my comfort. 912