The missing metal problem -: I.: How many metals are in submillimetre galaxies?

At redshifts larger than 2, a large fraction (80 per cent) of the metals is apparently as yet undetected. We use a sample of submillimetre-selected galaxies (SMGs) with molecular gas and dynamical mass measurements from the literature in order to put constraints on the contribution of such galaxies to the total metal budget. Compared with Lyman break galaxies (LBGs), for example, SMGs are rarer (by a factor of 10 or more), but contain much more gas and are more metal-rich. We estimate that SMGs brighter than 3 mJy contain only less than or similar to 9 per cent of the metals, when we combine the observed dynamical masses (< M-dyn> similar to few x 10(11) M-circle dot), number density (n similar or equal to 10(-4) Mpc(-3)), observed gas metallicity (Z similar or equal to 1-2 Z(circle dot)), and observed gas fractions (f(gas)approximate to 40 per cent), assuming a molecular to neutral hydrogen ratio of 1. Including SMGs fainter than 3 mJy, we estimate that SMGs contain about <= 15 per cent of the metals, where our incompleteness correction is estimated from the dust mass function. Our results are strong upper limits, given that high gas fractions and high overall metallicity are mutually exclusive. In summary, SMGs make a significant contribution to the metal budget (less than or similar to 15 per cent) but not sufficient to solve the 'missing metal problem'. A consequence of our results is that SMGs can only add approximate to 3.5 per cent to Omega(DLA), and cannot be the source of a significant population of dusty DLAs.