Is a 1.3V drop across P2N2222A normal?

I'm trying to power an IR led with a forward current of 100mA and attempting to control it with a P2N2222A.

The way I have it hooked up is:
5V -> LED
LED -> 22 ohm resistor -> P2N2222A[collector]
Arduino -> 1k ohm resistor -> P2N2222A[base]
P2N2222A[emitter] -> GND

Looking at it through a camera, it seemed quite dim compared to a TV remote. I figured out why - it's getting only 76mA.

Measured voltage drops 1.25 across the led, 1.68 across the resistor, and 1.3 across the transistor (collector to emitter), so the math works out fine; but why is my transistor eating up so much voltage?

According to what I've found on the internet, around 0.7V is to be expected
The manufacturer says 0.71 to 1.05 Volts Max @ 3.0 A, TJ = 150 C link

Should I be using a different component instead?

Not an ideal transistor for this particular job, a look at the datasheet:

Collector−Emitter Saturation Voltage (Note 1)   VCE(sat)  Min  Max   Unit
(IC = 150 mAdc, IB = 15 mAdc)                              -   0.2    Vdc
(IC = 500 mAdc, IB = 50 mAdc)                              -   1.0

And you have (at most) (5v - 0.6v)/1000ohm = 4.4mA base current

Try 270ohm instead of 1k for the base resistor.

Thanks, that worked like a charm; it's down to barely 0.1V and I'm getting 110mA.

Is the relationship between saturation voltage and IB linear? i.e. would it be safe to assume that I'll get a max drop of 0.2 + (IB-15) * (1.0-0.2)/(50-15), for values above 15mA?

For switching a transistor is best driven with base current of 5 to 10% of the collector current, since
you actually need to saturate the transistor, and saturation is nothing to do with the normal "DC current
gain" spec of a BJT, which applies to the forward active region only, where the collector-base junction is
reverse biased.

Saturation is extremely non-linear...

MarkT:
For switching a transistor is best driven with base current of 5 to 10% of the collector current, since
you actually need to saturate the transistor, and saturation is nothing to do with the normal "DC current
gain" spec of a BJT, which applies to the forward active region only, where the collector-base junction is
reverse biased.

I read that last part 5 times, think I need to go review a chapter or two..

OK, the "forward active region" is when the transistor acts as a transistor, amplifying current, and requires the
base-emitter junction to be reverse-biased, the base-emitter junction forward biased.

This is used for amplifying, for instance in an audio amplifier, and also in an emitter-follower buffer stage.

For use as a switch its not useful, you typically only use cut-off and saturation. (They are some subtleties to
do with saturation being slow to exit, which are important for high speed circuits, but for switching
high current loads at reasonable speeds you want saturation so the transistor doesn't waste lots of power
as heat).

Thanks for taking the time to explain Mark, really helped me out

Measured voltage drops 1.25 across the led, 1.68 across the resistor, and 1.3 across the transistor (collector to emitter),

This was a good thing to do.

Since you saw there was 1.3V from the collector to the emitter, you knew this transistor was not saturated.
Therefore you needed more base current (as you found out).

.